Chapter 12 Resource Masters - KTL MATH CLASSES . . . . . . . . . . . . . . . . . . . . . .A2–A39...
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Transcript of Chapter 12 Resource Masters - KTL MATH CLASSES . . . . . . . . . . . . . . . . . . . . . .A2–A39...
Chapter 12Resource Masters
Consumable WorkbooksMany of the worksheets contained in the Chapter Resource Masters bookletsare available as consumable workbooks.
Study Guide and Intervention Workbook 0-07-828029-XSkills Practice Workbook 0-07-828023-0Practice Workbook 0-07-828024-9
ANSWERS FOR WORKBOOKS The answers for Chapter 12 of these workbookscan be found in the back of this Chapter Resource Masters booklet.
Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Printed in the United States of America. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teacher, and families without charge; and be used solely in conjunction with Glencoe’s Algebra 2. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher.
Send all inquiries to:The McGraw-Hill Companies8787 Orion PlaceColumbus, OH 43240-4027
ISBN: 0-07-828015-X Algebra 2Chapter 12 Resource Masters
1 2 3 4 5 6 7 8 9 10 066 11 10 09 08 07 06 05 04 03 02
Glencoe/McGraw-Hill
© Glencoe/McGraw-Hill iii Glencoe Algebra 2
Contents
Vocabulary Builder . . . . . . . . . . . . . . . . vii
Lesson 12-1Study Guide and Intervention . . . . . . . . 699–700Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 701Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 702Reading to Learn Mathematics . . . . . . . . . . 703Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 704
Lesson 12-2Study Guide and Intervention . . . . . . . . 705–706Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 707Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 708Reading to Learn Mathematics . . . . . . . . . . 709Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 710
Lesson 12-3Study Guide and Intervention . . . . . . . . 711–712Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 713Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 714Reading to Learn Mathematics . . . . . . . . . . 715Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 716
Lesson 12-4Study Guide and Intervention . . . . . . . . 717–718Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 719Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 720Reading to Learn Mathematics . . . . . . . . . . 721Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 722
Lesson 12-5Study Guide and Intervention . . . . . . . . 723–724Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 725Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 726Reading to Learn Mathematics . . . . . . . . . . 727Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 728
Lesson 12-6Study Guide and Intervention . . . . . . . . 729–730Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 731Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 732Reading to Learn Mathematics . . . . . . . . . . 733Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 734
Lesson 12-7Study Guide and Intervention . . . . . . . . 735–736Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 737Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 738Reading to Learn Mathematics . . . . . . . . . . 739Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 740
Lesson 12-8Study Guide and Intervention . . . . . . . . 741–742Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 743Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 744Reading to Learn Mathematics . . . . . . . . . . 745Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 746
Lesson 12-9Study Guide and Intervention . . . . . . . . 747–748Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 749Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 750Reading to Learn Mathematics . . . . . . . . . . 751Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 752
Chapter 12 AssessmentChapter 12 Test, Form 1 . . . . . . . . . . . 753–754Chapter 12 Test, Form 2A . . . . . . . . . . 755–756Chapter 12 Test, Form 2B . . . . . . . . . . 757–758Chapter 12 Test, Form 2C . . . . . . . . . . 759–760Chapter 12 Test, Form 2D . . . . . . . . . . 761–762Chapter 12 Test, Form 3 . . . . . . . . . . . 763–764Chapter 12 Open-Ended Assessment . . . . . 765Chapter 12 Vocabulary Test/Review . . . . . . 766Chapter 12 Quizzes 1 & 2 . . . . . . . . . . . . . . 767Chapter 12 Quizzes 3 & 4 . . . . . . . . . . . . . . 768Chapter 12 Mid-Chapter Test . . . . . . . . . . . . 769Chapter 12 Cumulative Review . . . . . . . . . . 770Chapter 12 Standardized Test Practice . 771–772Unit 4 Test/Review (Ch. 11–12) . . . . . . 773–774
Standardized Test Practice Student Recording Sheet . . . . . . . . . . . . . . A1
ANSWERS . . . . . . . . . . . . . . . . . . . . . . A2–A39
© Glencoe/McGraw-Hill iv Glencoe Algebra 2
Teacher’s Guide to Using theChapter 12 Resource Masters
The Fast File Chapter Resource system allows you to conveniently file the resourcesyou use most often. The Chapter 12 Resource Masters includes the core materialsneeded for Chapter 12. These materials include worksheets, extensions, andassessment options. The answers for these pages appear at the back of this booklet.
All of the materials found in this booklet are included for viewing and printing in theAlgebra 2 TeacherWorks CD-ROM.
Vocabulary Builder Pages vii–viiiinclude a student study tool that presentsup to twenty of the key vocabulary termsfrom the chapter. Students are to recorddefinitions and/or examples for each term.You may suggest that students highlight orstar the terms with which they are notfamiliar.
WHEN TO USE Give these pages tostudents before beginning Lesson 12-1.Encourage them to add these pages to theirAlgebra 2 Study Notebook. Remind them to add definitions and examples as theycomplete each lesson.
Study Guide and InterventionEach lesson in Algebra 2 addresses twoobjectives. There is one Study Guide andIntervention master for each objective.
WHEN TO USE Use these masters asreteaching activities for students who needadditional reinforcement. These pages canalso be used in conjunction with the StudentEdition as an instructional tool for studentswho have been absent.
Skills Practice There is one master foreach lesson. These provide computationalpractice at a basic level.
WHEN TO USE These masters can be used with students who have weakermathematics backgrounds or needadditional reinforcement.
Practice There is one master for eachlesson. These problems more closely followthe structure of the Practice and Applysection of the Student Edition exercises.These exercises are of average difficulty.
WHEN TO USE These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.
Reading to Learn MathematicsOne master is included for each lesson. Thefirst section of each master asks questionsabout the opening paragraph of the lessonin the Student Edition. Additionalquestions ask students to interpret thecontext of and relationships among termsin the lesson. Finally, students are asked tosummarize what they have learned usingvarious representation techniques.
WHEN TO USE This master can be usedas a study tool when presenting the lessonor as an informal reading assessment afterpresenting the lesson. It is also a helpfultool for ELL (English Language Learner)students.
Enrichment There is one extensionmaster for each lesson. These activities mayextend the concepts in the lesson, offer anhistorical or multicultural look at theconcepts, or widen students’ perspectives onthe mathematics they are learning. Theseare not written exclusively for honorsstudents, but are accessible for use with alllevels of students.
WHEN TO USE These may be used asextra credit, short-term projects, or asactivities for days when class periods areshortened.
© Glencoe/McGraw-Hill v Glencoe Algebra 2
Assessment OptionsThe assessment masters in the Chapter 12Resource Masters offer a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use.
Chapter Assessment CHAPTER TESTS• Form 1 contains multiple-choice questions
and is intended for use with basic levelstudents.
• Forms 2A and 2B contain multiple-choicequestions aimed at the average levelstudent. These tests are similar in formatto offer comparable testing situations.
• Forms 2C and 2D are composed of free-response questions aimed at the averagelevel student. These tests are similar informat to offer comparable testingsituations. Grids with axes are providedfor questions assessing graphing skills.
• Form 3 is an advanced level test withfree-response questions. Grids withoutaxes are provided for questions assessinggraphing skills.
All of the above tests include a free-response Bonus question.
• The Open-Ended Assessment includesperformance assessment tasks that aresuitable for all students. A scoring rubricis included for evaluation guidelines.Sample answers are provided forassessment.
• A Vocabulary Test, suitable for allstudents, includes a list of the vocabularywords in the chapter and ten questionsassessing students’ knowledge of thoseterms. This can also be used in conjunc-tion with one of the chapter tests or as areview worksheet.
Intermediate Assessment• Four free-response quizzes are included
to offer assessment at appropriateintervals in the chapter.
• A Mid-Chapter Test provides an optionto assess the first half of the chapter. It iscomposed of both multiple-choice andfree-response questions.
Continuing Assessment• The Cumulative Review provides
students an opportunity to reinforce andretain skills as they proceed throughtheir study of Algebra 2. It can also beused as a test. This master includes free-response questions.
• The Standardized Test Practice offerscontinuing review of algebra concepts invarious formats, which may appear onthe standardized tests that they mayencounter. This practice includes multiple-choice, grid-in, and quantitative-comparison questions. Bubble-in andgrid-in answer sections are provided onthe master.
Answers• Page A1 is an answer sheet for the
Standardized Test Practice questionsthat appear in the Student Edition onpages 694–695. This improves students’familiarity with the answer formats theymay encounter in test taking.
• The answers for the lesson-by-lessonmasters are provided as reduced pageswith answers appearing in red.
• Full-size answer keys are provided forthe assessment masters in this booklet.
Reading to Learn MathematicsVocabulary Builder
NAME ______________________________________________ DATE ____________ PERIOD _____
1212
© Glencoe/McGraw-Hill vii Glencoe Algebra 2
Voca
bula
ry B
uild
erThis is an alphabetical list of the key vocabulary terms you will learn in Chapter 12.As you study the chapter, complete each term’s definition or description. Rememberto add the page number where you found the term. Add these pages to your AlgebraStudy Notebook to review vocabulary at the end of the chapter.
Vocabulary Term Found on Page Definition/Description/Example
binomial experiment
combination
compound event
dependent and independent events
inclusive events
ihn·KLOO·sihv
margin of sampling error
measure of central tendency
measure of variation
mutually exclusive events
MYOO·chuh·lee
normal distribution
(continued on the next page)
© Glencoe/McGraw-Hill viii Glencoe Algebra 2
Vocabulary Term Found on Page Definition/Description/Example
odds
permutation
PUHR·myoo·TAY·shuhn
probability
probability distribution
random variable
relative-frequency histogram
sample space
skewed distribution
SKYOOD
standard deviation
variance
VEHR·ee·uhn(t)s
Reading to Learn MathematicsVocabulary Builder (continued)
NAME ______________________________________________ DATE ____________ PERIOD _____
1212
Study Guide and InterventionThe Counting Principle
NAME ______________________________________________ DATE ____________ PERIOD _____
12-112-1
© Glencoe/McGraw-Hill 699 Glencoe Algebra 2
Less
on
12-
1
Independent Events If the outcome of one event does not affect the outcome ofanother event and vice versa, the events are called independent events.
Fundamental If event M can occur in m ways and is followed by event N that can occur in n ways, Counting Principle then the event M followed by the event N can occur in m � n ways.
FOOD For the Breakfast Special at the Country Pantry, customerscan choose their eggs scrambled, fried, or poached, whole wheat or white toast,and either orange, apple, tomato, or grapefruit juice. How many differentBreakfast Specials can a customer order?A customer’s choice of eggs does not affect his or her choice of toast or juice, so the eventsare independent. There are 3 ways to choose eggs, 2 ways to choose toast, and 4 ways tochoose juice. By the Fundamental Counting Principle, there are 3 � 2 � 4 or 24 ways tochoose the Breakfast Special.
Solve each problem.
1. The Palace of Pizza offers small, medium, or large pizzas with 14 different toppingsavailable. How many different one-topping pizzas do they serve? 42
2. The letters A, B, C, and D are used to form four-letter passwords for entering a computerfile. How many passwords are possible if letters can be repeated? 256
3. A restaurant serves 5 main dishes, 3 salads, and 4 desserts. How many different mealscould be ordered if each has a main dish, a salad, and a dessert? 60
4. Marissa brought 8 T-shirts and 6 pairs of shorts to summer camp. How many differentoutfits consisting of a T-shirt and a pair of shorts does she have? 48
5. There are 6 different packages available for school pictures. The studio offers 5 differentbackgrounds and 2 different finishes. How many different options are available? 60
6. How many 5-digit even numbers can be formed using the digits 4, 6, 7, 2, 8 if digits canbe repeated? 2500
7. How many license plate numbers consisting of three letters followed by three numbersare possible when repetition is allowed? 17,576,000
8. How many 4-digit positive even integers are there? 4500
ExampleExample
ExercisesExercises
© Glencoe/McGraw-Hill 700 Glencoe Algebra 2
Dependent Events If the outcome of an event does affect the outcome of another event,the two events are said to be dependent. The Fundamental Counting Principle still applies.
ENTERTAINMENT The guests at a sleepover brought 8 videos. Theydecided they would only watch 3 videos. How many orders of 3 different videosare possible?After the group chooses to watch a video, they will not choose to watch it again, so thechoices of videos are dependent events.
There are 8 choices for the first video. That leaves 7 choices for the second. After they choosethe first 2 videos, there are 6 remaining choices. Thus by the Fundamental CountingPrinciple, there are 8 � 7 � 6 or 336 orders of 3 different videos.
Solve each problem.
1. Three students are scheduled to give oral reports on Monday. In how many ways cantheir presentations be ordered? 6
2. In how many ways can the first five letters of the alphabet be arranged if each letter isused only once? 120
3. In how many different ways can 4 different books be arranged on the shelf? 24
4. How many license plates consisting of three letters followed by three numbers arepossible when no repetition is allowed? 11,232,000
5. Sixteen teams are competing in a soccer match. Gold, silver, and bronze medals will beawarded to the top three finishers. In how many ways can the medals be awarded? 3360
6. In a word-building game each player picks 7 letter tiles. If Julio’s letters are all different,how many 3-letter combinations can he make out of his 7 letters? 210
7. The editor has accepted 6 articles for the news letter. In how many ways can the 6 articlesbe ordered? 720
8. There are 10 one-hour workshops scheduled for the open house at the greenhouse.There is only one conference room available. In how many ways can the workshops beordered? 3,628,800
9. The top 5 runners at the cross-country meet will receive trophies. If there are 22 runnersin the race, in how many ways can the trophies be awarded? 3,160,080
Study Guide and Intervention (continued)
The Counting Principle
NAME ______________________________________________ DATE ____________ PERIOD _____
12-112-1
ExampleExample
ExercisesExercises
Skills PracticeThe Counting Principle
NAME ______________________________________________ DATE ____________ PERIOD _____
12-112-1
© Glencoe/McGraw-Hill 701 Glencoe Algebra 2
Less
on
12-
1
State whether the events are independent or dependent.
1. finishing in first, second, or third place in a ten-person race dependent
2. choosing a pizza size and a topping for the pizza independent
3. Seventy-five raffle tickets are placed in a jar. Three tickets are then selected, one afterthe other, without replacing a ticket after it is chosen. dependent
4. The 232 members of the freshman class all vote by secret ballot for the classrepresentative to the Student Senate. independent
Solve each problem.
5. A surveying firm plans to buy a color printer for printing its maps. It has narrowed itschoice to one of three models. Each of the models is available with either 32 megabytesof random access memory (RAM), 64 megabytes of RAM, or 128 megabytes of RAM.From how many combinations of models and RAM does the firm have to choose? 9
6. How many arrangements of three letters can be formed from the letters of the wordMATH if any letter will not be used more than once? 24
7. Allan is playing the role of Oliver in his school’s production of Oliver Twist. Thewardrobe crew has presented Allan with 5 pairs of pants and 4 shirts that he can wear.How many possible costumes consisting of a pair of pants and a shirt does Allan have tochoose from? 20
8. The 10-member steering committee that is preparing a study of the public transportationneeds of its town will select a chairperson, vice-chairperson, and secretary from thecommittee. No person can serve in more than one position. In how many ways can thethree positions be filled? 720
9. Jeanine has decided to buy a pickup truck. Her choices include either a V-6 engine or aV-8 engine, a standard cab or an extended cab, and 2-wheel drive or 4-wheel drive. Howmany possible models does she have to choose from? 8
10. A mail-order company that sells gardening tools offers rakes in two different lengths.Customers can also choose either a wooden, plastic, or fiberglass handle for the rake.How many different kinds of rakes can a customer buy? 6
11. A Mexican restaurant offers chicken, beef, or vegetarian fajitas wrapped with either cornor flour tortillas, and topped with either mild, medium, or hot salsa. How many differentchoices of fajitas does a customer have? 18
© Glencoe/McGraw-Hill 702 Glencoe Algebra 2
State whether the events are independent or dependent.
1. choosing an ice cream flavor and choosing a topping for the ice cream independent
2. choosing an offensive player of the game and a defensive player of the game in aprofessional football game independent
3. From 15 entries in an art contest, a camp counselor chooses first, second, and third placewinners. dependent
4. Jillian is selecting two more courses for her block schedule next semester. She mustselect one of three morning history classes and one of two afternoon math classes.independent
Solve each problem.
5. A briefcase lock has 3 rotating cylinders, each containing 10 digits. How many numericalcodes are possible? 1000
6. A golf club manufacturer makes irons with 7 different shaft lengths, 3 different grips, 5different lies, and 2 different club head materials. How many different combinations areoffered? 210
7. There are five different routes that a commuter can take from her home to the office. Inhow many ways can she make a round trip if she uses a different route coming thangoing? 20
8. In how many ways can the four call letters of a radio station be arranged if the firstletter must be W or K and no letters repeat? 27,600
9. How many 7-digit phone numbers can be formed if the first digit cannot be 0 or 1, andany digit can be repeated? 8,000,000
10. How many 7-digit phone numbers can be formed if the first digit cannot be 0, and anydigit can be repeated? 9,000,000
11. How many 7-digit phone numbers can be formed if the first digit cannot be 0 or 1, and ifno digit can be repeated? 483,840
12. How many 7-digit phone numbers can be formed if the first digit cannot be 0, and if nodigit can be repeated? 544,320
13. How many 6-character passwords can be formed if the first character is a digit and theremaining 5 characters are letters that can be repeated? 118,813,760
14. How many 6-character passwords can be formed if the first and last characters aredigits and the remaining characters are letters? Assume that any character can berepeated. 45,697,600
Practice (Average)
The Counting Principle
NAME ______________________________________________ DATE ____________ PERIOD _____
12-112-1
Reading to Learn MathematicsThe Counting Principle
NAME ______________________________________________ DATE ____________ PERIOD _____
12-112-1
© Glencoe/McGraw-Hill 703 Glencoe Algebra 2
Less
on
12-
1
Pre-Activity How can you count the maximum number of license plates a statecan issue?
Read the introduction to Lesson 12-1 at the top of page 632 in your textbook.
Assume that all Florida license plates have three letters followed by threedigits, and that there are no rules against using the same letter or numbermore than once. How many choices are there for each letter? for each digit?26; 10
Reading the Lesson
1. Shamim is signing up for her classes. Most of her classes are required, but she has twoelectives. For her arts class, she can chose between Art, Band, Chorus, or Drama. For herlanguage class, she can choose between French, German, and Spanish.
a. To organize her choices, Shamim decides to make a tree diagram. Let A, B, C, and Drepresent Art, Band, Chorus, and Drama, and F, G, and S represent French, German,and Spanish. Complete the following diagram.
b. How could Shamim have found the number of possible combinations without making atree diagram? Sample answer: Multiply the number of choices for herarts class by the number of choices for her language class: 3 � 4 �12.
2. A jar contains 6 red marbles, 4 blue marbles, and 3 yellow marbles. Indicate whether theevents described are dependent or independent.
a. A marble is drawn out of the jar and is not replaced. A second marble is drawn.dependent
b. A marble is drawn out of the jar and is put back in. The jar is shaken. A secondmarble is drawn. independent
Helping You Remember
3. One definition of independent is “not determined or influenced by someone or somethingelse.” How can this definition help you remember the difference between independentand dependent events? Sample answer: If the outcome of one event does notaffect or influence the outcome of another, the events are independent. Ifthe outcome of one event does affect or influence the outcome ofanother, the events are dependent.
© Glencoe/McGraw-Hill 704 Glencoe Algebra 2
Tree Diagrams and the Power RuleIf you flip a coin once, there are two possible outcomes: heads showing (H) or tails showing (T).The tree diagram to the right shows the four (22)possible outcomes if you flip a coin twice.
Flip 2
HTHT
Flip 1
H
T
Outcomes
HHHTTHTT
start
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
12-112-1
Draw a tree diagram toshow all the possible outcomes for flippinga coin three times. List the outcomes.
There are eight (23) possible outcomes. Witheach extra flip, the number of outcomes doubles. With 4 flips, there would be sixteen(24) outcomes.
Flip 2
H
T
H
T
Flip 1
H
T
Flip 3
HTHTHTHT
Outcomes
HHHHHTHTHHTTTHHTHTTTHTTT
start
In a cup there are ared, a blue, and a yellow marble. Howmany possible outcomes are there ifyou draw one marble at random,replace it, and then draw another?
There are nine (32) possible outcomes.
Draw 2
RBYRBYRBY
Outcomes
RRRBRYBRBBBYYRYBYY
Draw 1
R
B
Y
start
Example 1Example 1 Example 2Example 2
The Power Rule for the number of outcomes states that if an experiment isrepeated n times, and if there are b possible outcomes each time, there are bn total possible outcomes.
Find the total number of possible outcomes for each experiment. Usetree diagrams to help you.
1. flipping a coin 5 times 2. doing the marble experiment 6 times
3. flipping a coin 8 times 4. rolling a 6-sided die 2 times
5. rolling a 6-sided die 3 times 6. rolling a 4-sided die 2 times
7. rolling a 4-sided die 3 times 8. rolling a 12-sided die 2 times
Study Guide and InterventionPermutations and Combinations
NAME ______________________________________________ DATE ____________ PERIOD _____
12-212-2
© Glencoe/McGraw-Hill 705 Glencoe Algebra 2
Less
on
12-
2
Permutations When a group of objects or people are arranged in a certain order, thearrangement is called a permutation.
Permutations The number of permutations of n distinct objects taken r at a time is given by P(n, r ) � .
Permutations with Repetitions
The number of permutations of n objects of which p are alike and q are alike is .
The rule for permutations with repetitions can be extended to any number of objects thatare repeated.
From a list of 20 books, each student must choose 4 books for bookreports. The first report is a traditional book report, the second a poster, the thirda newspaper interview with one of the characters, and the fourth a timeline of theplot. How many different orderings of books can be chosen?Since each book report has a different format, order is important. You must find the numberof permutations of 20 objects taken 4 at a time.
P(n, r) � Permutation formula
P(20, 4) � n � 20, r � 4
� Simplify.
� Divide by common factors.
� 116,280Books for the book reports can be chosen 116,280 ways.
Evaluate each expression.
1. P(6, 3) 120 2. P(8, 5) 6720 3. P(9, 4) 3024 4. P(11, 6) 332,640
How many different ways can the letters of each word be arranged?
5. MOM 3 6. MONDAY 720 7. STEREO 360
8. SCHOOL The high school chorus has been practicing 12 songs, but there is time for only5 of them at the spring concert. How may different orderings of 5 songs are possible?95,040
20 � 19 � 18 � 17 � 16 � 15 � … � 1����16 � 15 � … � 1
20!�16!
20!��(20 � 4)!
n!�(n � r)!
n!�p !q !
n!�(n � r )!
ExampleExample
ExercisesExercises
1 1 1
1 1 1
© Glencoe/McGraw-Hill 706 Glencoe Algebra 2
Combinations An arrangement or selection of objects in which order is not important iscalled a combination.
Combinations The number of combinations of n distinct objects taken r at a time is given by C(n, r ) � .
SCHOOL How many groups of 4 students can be selected from aclass of 20?Since the order of choosing the students is not important, you must find the number ofcombinations of 20 students taken 4 at a time.
C(n, r) � Combination formula
C(20, 4) � n � 20, r � 4
� or 4845
There are 4845 possible ways to choose 4 students.
In how many ways can you choose 1 vowel and 2 consonants from aset of 26 letter tiles? (Assume there are 5 vowels and 21 consonants.)By the Fundamental Counting Principle, you can multiply the number of ways to select onevowel and the number of ways to select 2 consonants. Only the letters chosen matter, notthe order in which they were chosen, so use combinations.
C(5, 1) One of 5 vowels are drawn.C(21, 2) Two of 21 consonants are drawn.
C(5, 1) � C(21, 2) � � Combination formula
� � Subtract.
� 5 � 210 or 1050 Simplify.
There are 1050 combinations of 1 vowel and 2 consonants.
Evaluate each expression.
1. C(5, 3) 10 2. C(7, 4) 35 3. C(15, 7) 6435 4. C(10, 5) 252
5. PLAYING CARDS From a standard deck of 52 cards, in how many ways can 5 cards bedrawn? 2,598,960
6. HOCKEY How many hockey teams of 6 players can be formed from 14 players withoutregard to position played? 3003
7. COMMITTEES From a group of 10 men and 12 women, how many committees of 5 menand 6 women can be formed? 232,848
21!�19!2!
5!�4!
21!��(21 � 2)!2!
5!��(5 � 1)!1!
20!�16!4!
20!��(20 � 4)!4!
n!��(n � r)!r!
n !��(n � r )!r !
Study Guide and Intervention (continued)
Permutations and Combinations
NAME ______________________________________________ DATE ____________ PERIOD _____
12-212-2
Example 1Example 1
Example 2Example 2
ExercisesExercises
Skills PracticePermutations and Combinations
NAME ______________________________________________ DATE ____________ PERIOD _____
12-212-2
© Glencoe/McGraw-Hill 707 Glencoe Algebra 2
Less
on
12-
2
Evaluate each expression.
1. P(6, 3) 120 2. P(8, 2) 56 3. P(2, 1) 2
4. P(3, 2) 6 5. P(10, 4) 5040 6. P(5, 5) 120
7. C(2, 2) 1 8. C(5, 3) 10 9. C(4, 1) 4
10. C(8, 7) 8 11. C(3, 2) 3 12. C(7, 4) 35
Determine whether each situation involves a permutation or a combination. Thenfind the number of possibilities.
13. seating 8 students in 8 seats in the front row of the school auditoriumpermutation; 40,320
14. introducing the 5 starting players on the Woodsville High School basketball team at thebeginning of the next basketball gamepermutation; 120
15. checking out 3 library books from a list of 8 books for a research papercombination; 56
16. choosing 2 movies to rent from 5 moviescombination; 10
17. the first-, second-, and third-place finishers in a race with 10 contestantspermutation; 720
18. electing 4 candidates to a municipal planning board from a field of 7 candidatescombination; 35
19. choosing 2 vegetables from a menu that offers 6 vegetable choicescombination; 15
20. an arrangement of the letters in the word rhombuspermutation; 5040
21. selecting 2 of 8 choices of orange juice at a storecombination; 28
22. placing a red rose bush, a yellow rose bush, a white rose bush, and a pink rose bush in arow in a planter permutation; 24
23. selecting 2 of 9 kittens at an animal rescue sheltercombination; 36
24. an arrangement of the letters in the word isoscelespermutation; 30,240
© Glencoe/McGraw-Hill 708 Glencoe Algebra 2
Evaluate each expression.
1. P(8, 6) 20,160 2. P(9, 7) 181,440 3. P(3, 3) 6
4. P(4, 3) 24 5. P(4, 1) 4 6. P(7, 2) 42
7. C(8, 2) 28 8. C(11, 3) 165 9. C(20, 18) 190
10. C(9, 9) 1 11. C(3, 1) 3 12. C(9, 3) � C(6, 2) 1260
Determine whether each situation involves a permutation or a combination. Thenfind the number of possibilities.
13. selecting a 4-person bobsled team from a group of 9 athletescombination; 126
14. an arrangement of the letters in the word Canadapermutation; 120
15. arranging 4 charms on a bracelet that has a clasp, a front, and a backpermutation; 24
16. selecting 3 desserts from 10 desserts that are displayed on a dessert cart in a restaurantcombination; 120
17. an arrangement of the letters in the word annuallypermutation; 5040
18. forming a 2-person sales team from a group of 12 salespeoplecombination; 66
19. making 5-sided polygons by choosing any 5 of 11 points located on a circle to be the verticescombination; 462
20. seating 5 men and 5 women alternately in a row, beginning with a womanpermutation; 14,400
21. STUDENT GROUPS Farmington High is planning its academic festival. All mathclasses will send 2 representatives to compete in the math bowl. How many differentgroups of students can be chosen from a class of 16 students? 120
22. PHOTOGRAPHY A photographer is taking pictures of a bride and groom and their 6attendants. If she takes photographs of 3 people in a group, how many different groupscan she photograph? 56
23. AIRLINES An airline is hiring 5 flight attendants. If 8 people apply for the job, howmany different groups of 5 attendants can the airline hire? 56
24. SUBSCRIPTIONS A school librarian would like to buy subscriptions to 7 newmagazines. Her budget, however, will allow her to buy only 4 new subscriptions. Howmany different groups of 4 magazines can she choose from the 7 magazines? 35
Practice (Average)
Permutations and Combinations
NAME ______________________________________________ DATE ____________ PERIOD _____
12-212-2
Reading to Learn MathematicsPermutations and Combinations
NAME ______________________________________________ DATE ____________ PERIOD _____
12-212-2
© Glencoe/McGraw-Hill 709 Glencoe Algebra 2
Less
on
12-
2
Pre-Activity How do permutations and combinations apply to softball?
Read the introduction to Lesson 12-2 at the top of page 638 in your textbook.
Suppose that 20 students enter a math contest. In how many ways canfirst, second, and third places be awarded? (Write your answer as a product.Do not calculate the product.) 20 � 19 � 18
Reading the Lesson
1. Indicate whether each situation involves a permutation or a combination.
a. choosing five students from a class to work on a special project combination
b. arranging five pictures in a row on a wall permutation
c. drawing a hand of 13 cards from a 52-card deck combination
d. arranging the letters of the word algebra permutation
2. Write an expression that can be used to calculate each of the following.
a. number of combinations of n distinct objects taken r at a time �(n �
n!r)!r!�
b. number of permutations of n objects of which p are alike and q are alike �pn!q!!
�
c. number of permutations of n distinct objects taken r at a time �(n �
n!r)!
�
3. Five cards are drawn from a standard deck of cards. Suppose you are asked to determinehow many possible hands consist of one heart, two diamonds, and two spades.
a. Which of the following would you use to solve this problem: Fundamental CountingPrinciple, permutations, or combinations? (More than one of these may apply.)
Fundamental Counting Principle, combinations
b. Write an expression that involves the notation P(n, r) and/or C(n, r) that you would useto solve this problem. (Do not do any calculations.)
C(13, 1) � C(13, 2) � C(13, 2)
Helping You Remember
4. Many students have trouble knowing when to use permutations and when to usecombinations to solve counting problems. How can the idea of order help you toremember the difference between permutations and combinations?
Sample answer: A permutation is an arrangement of objects in whichorder is important. A combination is a selection of objects in which orderis not important.
© Glencoe/McGraw-Hill 710 Glencoe Algebra 2
Combinations and Pascal’s TrianglePascal’s triangle is a special array of numbers invented by Blaise Pascal(1623–1662). The values in Pascal’s triangle can be found using thecombinations shown below.
1. Evaluate the expression in each cell of the triangle.
2. The pattern shows the relationship between C(n, r) and Pascal’s triangle. Ingeneral, it is true that C(n, r) � C(n, r � 1) � C(n � 1, r � 1). Completethe proof of this property. In each step, the denominator has been given.
C(n, r) � C(n, r � 1) � �
� �
� �
�
�
�
�
� C(n � 1, r � 1)
(r � 1)![(n � 1) � (r � 1)]!
(r � 1)!(n � r)!
(r � 1)!(n � r)!
(r � 1)!(n � r)!
(r � 1)!(n � r)!(r � 1)!(n � r)!
(r � 1)!(n � r � 1)!(n � r)r!(n � r)!(r � 1)
(r � 1)!(n � r � 1)!r!(n � r)!
C(1,0) C(1,1)
C(2,0) C(2,1) C(2,2)
C(3,0) C(3,1) C(3,2) C(3,3)
C(4,0) C(4,1) C(4,2) C(4,3) C(4,4)
C(5,0) C(5,1) C(5,2) C(5,3) C(5,4) C(5,5)
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
12-212-2
Study Guide and InterventionProbability
NAME ______________________________________________ DATE ____________ PERIOD _____
12-312-3
© Glencoe/McGraw-Hill 711 Glencoe Algebra 2
Less
on
12-
3
Probability and Odds In probability, a desired outcome is called a success; any otheroutcome is called a failure.
Probability of If an event can succeed in s ways and fail in f ways, then the probabilities of success, P (S ),
Success and and of failure, P (F), are as follows.
Failure P (S ) � and P (F) � .
DefinitionIf an event can succeed in s ways and fail in f ways, then the odds of success and of failure are
of Oddsas follows.Odds of success � s :f Odds of failure � f :s
When 3 coins are tossed, what is the probability that at least 2 are heads?
You can use a tree diagram to find the sample space.Of the 8 possible outcomes, 4 have at least 2 heads. So the
probability of tossing at least 2 heads is �48� or �
12�.
What is the probability of picking 4 fiction books and 2 biographiesfrom a best-seller list that consists of 12 fiction books and 6 biographies?By the Fundamental Counting Principle, the number of successes is C(12, 4) � C(6, 2).The total number of selections, s � f, of 6 books is C(18, 6).
P(4 fiction, 2 biography) � or about 0.40
The probability of selecting 4 fiction books and 2 biographies is about 40%.
Find the odds of an event occurring, given the probability of the event.
1. �37� 3:4 2. �
45� 4:1 3. �1
23� 2:11 4. 1:14
Find the probability of an event occurring, given the odds of the event.
5. 10:1 �1101� 6. 2:5 �
27
� 7. 4:9 �143� 8. 8:3 �
181�
One bag of candy contains 15 red candies, 10 yellow candies, and 6 green candies.Find the probability of each selection.
9. picking a red candy �1351� 10. not picking a yellow candy �
2311�
11. picking a green candy �361� 12. not picking a red candy �
1361�
1�15
C(12, 4) � C(6, 2)��C(18, 6)
HHHHHTHTHHTTTHHTHTTTHTTT
HTHTHTHT
H
T
H
T
H
T
FirstCoin
SecondCoin
ThirdCoin
PossibleOutcomes
f�s � f
s�s � f
Example 1Example 1
Example 2Example 2
ExercisesExercises
© Glencoe/McGraw-Hill 712 Glencoe Algebra 2
Probability Distributions A random variable is a variable whose value is thenumerical outcome of a random event. A probability distribution for a particular randomvariable is a function that maps the sample space to the probabilities of the outcomes in thesample space.
Suppose two dice are rolled. The table and the relative-frequencyhistogram show the distribution of the absolute value of the difference of thenumbers rolled. Use the graph to determine which outcome is the most likely.What is its probability?
The greatest probability in the graph is �14�.
The most likely outcome is a difference of 1 and its
probability is �14�.
Four coins are tossed.
1. Complete the table below to show the probability distribution of the number of heads.
2. Make relative-frequency distribution of the data.
10Heads
Heads in Coin Toss
2 3 4
14
Pro
bab
ility
38
18
116
316
516
Number of Heads 0 1 2 3 4
Probability �116� �
14
� �38
� �14
� �116�
14
00
Pro
bab
ility
Difference
Numbers Showing on the Dice
1 2 3 4 5
16
112
Difference 0 1 2 3 4 5
Probability �16
� �14
� �16
� �16
� �16
� �112�
Study Guide and Intervention (continued)
Probability
NAME ______________________________________________ DATE ____________ PERIOD _____
12-312-3
ExampleExample
ExercisesExercises
Skills PracticeProbability
NAME ______________________________________________ DATE ____________ PERIOD _____
12-312-3
© Glencoe/McGraw-Hill 713 Glencoe Algebra 2
Less
on
12-
3
Ahmed is posting 2 photographs on his website. He has narrowed his choices to 4landscape photographs and 3 portraits. If he chooses the two photographs atrandom, find the probability of each selection.
1. P(2 portrait) �17
� 2. P(2 landscape) �27
� 3. P(1 of each) �47
�
The Carubas have a collection of 28 video movies, including 12 westerns and 16 science fiction. Elise selects 3 of the movies at random to bring to a sleep-overat her friend’s house. Find the probability of each selection.
4. P(3 westerns) �85159
� 5. P(3 science fiction) �12107
�
6. P(1 western and 2 science fiction) �4901� 7. P(2 westerns and 1 science fiction) �
28783
�
8. P(3 comedy) 0 9. P(2 science fiction and 2 westerns) 0
For Exercises 10–13, use the chart that shows the class and gender statistics for the students taking an Algebra 1 or Algebra 2 class at La Mesa High School.If a student taking Algebra 1 or Algebra 2 is selected at random, find each probability. Express as decimals rounded to the nearest thousandth.
10. P(sophomore/female) 0.208
11. P(junior/male) 0.143
12. P(freshman/male) 0.136
13. P(freshman/female) 0.145
Find the odds of an event occurring, given the probability of the event.
14. �58� 5:3 15. �
27� 2:5 16. �
35� 3:2
17. �110� 1:9 18. �
56� 5:1 19. �1
52� 5:7
Find the probability of an event occurring, given the odds of the event.
20. 2:1 �23
� 21. 8:9 �187� 22. 4:1 �
45
�
23. 1:9 �110� 24. 2:7 �
29
� 25. 5:9 �154�
Class/Gender Number
Freshman/Male 95
Freshman/Female 101
Sophomore/Male 154
Sophomore/Female 145
Junior/Male 100
Junior/Female 102
© Glencoe/McGraw-Hill 714 Glencoe Algebra 2
A bag contains 1 green, 4 red, and 5 yellow balls. Two balls are selected atrandom. Find the probability of each selection.
1. P(2 red) �125� 2. P(1 red and 1 yellow) �
49
� 3. P(1 green and 1 yellow) �19
�
4. P(2 green) 0 5. P(2 red and 1 yellow) 0 6. P(1 red and 1 green) �445�
A bank contains 3 pennies, 8 nickels, 4 dimes, and 10 quarters. Two coins areselected at random. Find the probability of each selection.
7. P(2 pennies) �1100� 8. P(2 dimes) �
510� 9. P(1 nickel and 1 dime) �
785�
10. P(1 quarter and 1 penny) 11. P(1 quarter and 1 nickel) 12. P(2 dimes and 1 quarter)
�110� �
145� 0
Henrico visits a home decorating store to choose wallpapers for his new house. Thestore has 28 books of wallpaper samples, including 10 books of WallPride samplesand 18 books of Deluxe Wall Coverings samples. The store will allow Henrico tobring 4 books home for a few days so he can decide which wallpapers he wants tobuy. If Henrico randomly chooses 4 books to bring home, find the probability ofeach selection.
13. P(4 WallPride) �1295� 14. P(2 WallPride and 2 Deluxe) �
145535
�
15. P(1 WallPride and 3 Deluxe) �1534645
� 16. P(3 WallPride and 1 Deluxe) �44585
�
For Exercises 17–20, use the table that shows the range of verbal SAT scores forfreshmen at a small liberalarts college. If a freshman student is chosen at random, find each probability.Express as decimals rounded to the nearest thousandth.
17. P(400–449) 0.052 18. P(550–559) 0.243 19. P(at least 650) 0.166
Find the odds of an event occurring, given the probability of the event.
20. �141� 4:7 21. �
1123� 12:1 22. �9
59� 5:94 23. �10
100� 1:999
24. �156� 5:11 25. �9
35� 3:92 26. �7
90� 9:61 27. �1
85� 8:7
Find the probability of an event occurring, given the odds of the event.
28. 2:23 �225� 29. 2:5 �
27
� 30. 15:1 �1156� 31. 9:7 �
196�
32. 11:14 �1215� 33. 1000:1 �
11000001
� 34. 12:17 �1229� 35. 8:13 �
281�
Range 400–449 450–499 500–549 550–559 600–649 650�
Number of Students
129 275 438 602 620 412
Practice (Average)
Probability
NAME ______________________________________________ DATE ____________ PERIOD _____
12-312-3
Reading to Learn MathematicsProbability
NAME ______________________________________________ DATE ____________ PERIOD _____
12-312-3
© Glencoe/McGraw-Hill 715 Glencoe Algebra 2
Less
on
12-
3
Pre-Activity What do probability and odds tell you about life’s risks?
Read the introduction to Lesson 12-3 at the top of page 644 in your textbook.
What is the probability that a person will not be struck by lightning in agiven year?
�774590,,909090
�
Reading the Lesson
1. Indicate whether each of the following statements is true or false.
a. If an event can never occur, its probability is a negative number. false
b. If an event is certain to happen, its probability is 1. true
c. If an event can succeed in s ways and fail in f ways, then the probability of success
is . false
d. If an event can succeed in s ways and fail in f ways, then the odds against the eventare s :f. false
e. A probability distribution is a function in which the domain is the sample space of anexperiment. true
2. A weather forecast says that the chance of rain tomorrow is 40%.
a. Write the probability that it will rain tomorrow as a fraction in lowest terms. �25
�
b. Write the probability that it will not rain tomorrow as a fraction in lowest terms. �35
�
c. What are the odds in favor of rain? 2:3
d. What are the odds against rain? 3:2
3. Refer to the table in Example 4 on page 646 in your textbook.
a. What other sum has the same probability as a sum of 11? 3
b. What are the odds of rolling a sum of 8? 5:31
c. What are the odds against rolling a sum of 9? 8:1
Helping You Remember
4. A good way to remember something is to explain it to someone else. Suppose that yourfriend Roberto is having trouble remembering the difference between probability andodds. What would you tell him to help him remember this easily?
Sample answer: Probability gives the ratio of successes to the totalnumber of outcomes, while odds gives the ratio of successes to failures.
s�f
© Glencoe/McGraw-Hill 716 Glencoe Algebra 2
Geometric ProbabilityIf a dart, thrown at random, hits the triangular board shown at the right, what is the chance that it will hit the shaded region? This chance, also called a probability, can be determined by comparing the area of the shaded region to the area of the board. This ratio indicates what fraction of the tosses should hit in the shaded region.
�
� �1224� or �
12�
In general, if S is a subregion of some region R, then the probability,P(S), that a point, chosen at random, belongs to subregion S is given by the following.
P(S) �
Find the probability that a point, chosen at random, belongs to theshaded subregions of the following regions.
1. �12
� 2. �59
� 3. ��4
�
The dart board shown at the right has 5 concentric circles whose centers are also the center of the square board. Each side of the board is 38 cm, and the radii of the circles are 2 cm, 5 cm, 8 cm, 11 cm, and 14 cm. A dart hitting within one of the circular regions scores the number of points indicated on the board, while a hit anywhere else scores 0 points. If a dart, thrown at random, hits the board, find the probability of scoring the indicated number of points.
4. 0 points 5. 1 point 6. 2 points
�361
3�61
49�� �
17454�4
� �15474�4
�
7. 3 points 8. 4 points 9. 5 points
�13494�4
� �12414�4
� �3
�61�
51
2
34
4 4
4
4
46
6
64
4
3 3
5
5
area of subregion S���are of region R
�12
�(4)(6)��12
�(8)(6)
area of shaded region���area of triangular board
4 4
6
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
12-312-3
Study Guide and InterventionMultiplying Probabilities
NAME ______________________________________________ DATE ____________ PERIOD _____
12-412-4
© Glencoe/McGraw-Hill 717 Glencoe Algebra 2
Less
on
12-
4
Probability of Independent Events
Probability of Two If two events, A and B, are independent, then the probability of both occurring isIndependent Events P(A and B) � P(A) � P(B).
In a board game each player has 3 different-colored markers. To move around the board the player first spins a spinner to determine which piece can be moved. He or she then rolls a die to determine how many spacesthat colored piece should move. On a given turn what is theprobability that a player will be able to move the yellow piece more than 2 spaces?Let A be the event that the spinner lands on yellow, and let B be the event that the die
shows a number greater than 2. The probability of A is �13�, and the probability of B is �
23�.
P(A and B) � P(A) � P(B) Probability of independent events
� �13� � �
23� or �
29� Substitute and multiply.
The probability that the player can move the yellow piece more than 2 spaces is �29�.
A die is rolled 3 times. Find the probability of each event.
1. a 1 is rolled, then a 2, then a 3 �2116�
2. a 1 or a 2 is rolled, then a 3, then a 5 or a 6 �514�
3. 2 odd numbers are rolled, then a 6 �214�
4. a number less than 3 is rolled, then a 3, then a number greater than 3 �316�
5. A box contains 5 triangles, 6 circles, and 4 squares. If a figure is removed, replaced, anda second figure is picked, what is the probability that a triangle and then a circle will be picked? �
125� or about 0.13
6. A bag contains 5 red marbles and 4 white marbles. A marble is selected from the bag,then replaced, and a second selection is made. What is the probability of selecting 2 redmarbles? �
2851� or about 0.31
7. A jar contains 7 lemon jawbreakers, 3 cherry jawbreakers, and 8 rainbow jawbreakers.What is the probability of selecting 2 lemon jawbreakers in succession providing thejawbreaker drawn first is then replaced before the second is drawn?
�34294
� or about 0.15
blue
redyellow
ExampleExample
ExercisesExercises
© Glencoe/McGraw-Hill 718 Glencoe Algebra 2
Probability of Dependent Events
Probability of Two If two events, A and B, are dependent, then the probability of both events occurring isDependent Events P (A and B ) � P (A) � P (B following A).
There are 7 dimes and 9 pennies in a wallet. Suppose two coins areto be selected at random, without replacing the first one. Find the probability ofpicking a penny and then a dime.Because the coin is not replaced, the events are dependent.
Thus, P(A and B) � P(A) � P(B following A).P(penny, then dime) � P(penny) � P(dime following penny)
�196� � �1
75� � �
2810�
The probability is �2810� or about 0.26
What is the probability of drawing, without replacement, 3 hearts,then a spade from a standard deck of cards?Since the cards are not replaced, the events are dependent. Let H represent a heart and Srepresent a spade.
P(H, H, H, S) � P(H) � P(H following H) � P(H following 2 Hs) � P(S following 3 Hs)
� �1532� � �
1521� � �
1510� � �
1439� or about 0.003
The probability is about 0.003 of drawing 3 hearts, then a spade.
Find each probability.
1. The cup on Sophie’s desk holds 4 red pens and 7 black pens. What is the probability ofher selecting first a black pen, then a red one? �
1545� or about 0.25
2. What is the probability of drawing two cards showing odd numbers from a set of cardsthat show the first 20 counting numbers if the first card is not replaced before thesecond is chosen? �
398� or about 0.24
3. There are 3 quarters, 4 dimes, and 7 nickels in a change purse. Suppose 3 coins areselected without replacement. What is the probability of selecting a quarter, then a dime,and then a nickel? �
216� or about 0.04
4. A basket contains 4 plums, 6 peaches, and 5 oranges. What is the probability of picking 2 oranges, then a peach if 3 pieces of fruit are selected at random? �
941� or about 0.04
5. A photographer has taken 8 black and white photographs and 10 color photographs for abrochure. If 4 photographs are selected at random, what is the probability of picking first2 black and white photographs, then 2 color photographs? �
1702� or about 0.07
Study Guide and Intervention (continued)
Multiplying Probabilities
NAME ______________________________________________ DATE ____________ PERIOD _____
12-412-4
Example 1Example 1
Example 2Example 2
ExercisesExercises
Skills PracticeMultiplying Probabilities
NAME ______________________________________________ DATE ____________ PERIOD _____
12-412-4
© Glencoe/McGraw-Hill 719 Glencoe Algebra 2
Less
on
12-
4
A die is rolled twice. Find each probability.
1. P(5, then 6) �316� 2. P(no 2s) �
2356� 3. P(two 1s) �
316�
4. P(any number, then not 5) �56
� 5. P(4, then not 6) �356� 6. P(not 1, then not 2) �
2356�
A board game uses a set of 6 different cards. Each card displays one of the followingfigures: a star, a square, a circle, a diamond, a rectangle, or a pentagon. The cardsare placed face down, and a player chooses two cards. Find each probability.
7. P(circle, then star), if no replacement occurs �310�
8. P(diamond, then square), if replacement occurs �316�
9. P(2 polygons), if replacement occurs �2356�
10. P(2 polygons), if no replacement occurs �23
�
11. P(circle, then hexagon), if no replacement occurs 0
Determine whether the events are independent or dependent. Then find eachprobability.
12. A mixed box of herbal teabags contains 2 lemon teabags, 3 orange-mango teabags,3 chamomile teabags, and 1 apricot-ginger teabag. Kevin chooses 2 teabags at random tobring to work with him. What is the probability that he first chooses a lemon teabag andthen a chamomile teabag? dependent; �
112�
13. The chart shows the selection of olive oils that Hasha finds in a specialty foods catalog. If sherandomly selects one type of oil, then randomlyselects another, different oil, what is the probability that both selections are domestic,first cold pressed oils? dependent; �8
2210
�
For Exercises 14 and 15, two thirds of the area of the spinner earns you 50 points. Suppose you spin the spinner twice.
14. Sketch a tree diagram showing all of the possibilities. Use it to find the probability ofspinning 50 points, then 100 points. �
29
�
15. What is the probability that you get 100 points on each spin? �
19
�
100
50
Type of Oil Domestic Imported
Pure 2 5
Cold Pressed 4 8
First Cold Pressed 7 15
© Glencoe/McGraw-Hill 720 Glencoe Algebra 2
A die is rolled three times. Find each probability.
1. P(three 4s) �2116� 2. P(no 4s) �
122156
�
3. P(2, then 3, then 1) �2116� 4. P(three different even numbers) �
316�
5. P(any number, then 5, then 5) �316� 6. P(even number, then odd number, then 1) �
214�
There are 3 nickels, 2 dimes, and 5 quarters in a purse. Three coins are selected insuccession at random. Find the probability.
7. P(nickel, then dime, then quarter), if no replacement occurs �214�
8. P(nickel, then dime, then quarter), if replacement occurs �1300�
9. P(2 nickels, then 1 quarter), if no replacement occurs �214�
10. P(3 dimes), if replacement occurs �1125�
11. P(3 dimes), if no replacement occurs 0
For Exercises 12 and 13, determine whether the events are independent ordependent. Then find each probability.
12. Serena is creating a painting. She wants to use 2 more colors. She chooses randomly from6 shades of red, 10 shades of green, 4 shades of yellow, 4 shades of purple, and 6 shadesof blue. What is the probability that she chooses 2 shades of green? dependent; �
239�
13. Kershel’s mother is shopping at a bakery. The owner offers Kershel a cookie from a jarcontaining 22 chocolate chip cookies, 18 sugar cookies, and 15 oatmeal cookies. Withoutlooking, Kershel selects one, drops it back in, and then randomly selects another. What isthe probability that neither selection was a chocolate chip cookie? independent; �
295�
14. METEOROLOGY The Fadeeva’s are planning a 3-day vacation to the mountains. Along-range forecast reports that the probability of rain each day is 10%. Assuming thatthe daily probabilities of rain are independent, what is the probability that there is norain on the first two days, but that it rains on the third day? �
180100�
RANDOM NUMBERS For Exercises 15 and 16, use the following information.Anita has a list of 20 jobs around the house to do, and plans to do 3 of them today. She assigns each job a number from 1 to 20, andsets her calculator to generate random numbers from 1 to 20, whichcan reoccur. Of the jobs, 3 are outside, and the rest are inside.
15. Sketch a tree diagram showing all of the possibilities that the first three numbers generated correspond to inside jobs or outside jobs. Use it to find the probability that the first two numbers correspond to inside jobs,and the third to an outside job. 0.108375
16. What is the probability that the number generated corresponds to an outside job three times in a row? 0.003375
Practice (Average)
Multiplying Probabilities
NAME ______________________________________________ DATE ____________ PERIOD _____
12-412-4
Reading to Learn MathematicsMultiplying Probabilities
NAME ______________________________________________ DATE ____________ PERIOD _____
12-412-4
© Glencoe/McGraw-Hill 721 Glencoe Algebra 2
Less
on
12-
4
Pre-Activity How does probability apply to basketball?
Read the introduction to Lesson 12-4 at the top of page 651 in your textbook.
Write the probability that Reggie Miller made a free-throw shot during the1998�99 season as a fraction in lowest terms. (Your answer should notinclude a decimal.) �
128030
�
Reading the Lesson
1. A bag contains 4 yellow balls, 5 red balls, 1 white ball, and 2 black balls. A ball is drawnfrom the bag and is not replaced. A second ball is drawn.
a. Let Y be the event “first ball is yellow” and B be the event “second ball is black.” Arethese events independent or dependent? dependent
b. Tell which formula you would use to find the probability that the first ball is yellowand the second ball is black. C
A. P(Y and B) �
B. P(Y and B) � P(Y) � P(B)
C. P(Y and B) � P(Y) � P(B following Y)
c. Which equation shows the correct calculation of this probability? B
A. �13� � �1
21� � �
1373� B. �
13� � �1
21� � �3
23�
C. �13� � �
16� � �
12� D. �
13� � �
16� � �1
18�
d. Which equation shows the correct calculation of the probability that if three balls aredrawn in succession without replacement, all three will be red? B
A. �152� � �1
52� � �1
52� � �1
172258� B. �1
52� � �1
41� � �1
30� � �2
12�
C. �152� � �1
41� � �1
30� � �
761630�
Helping You Remember
2. Some students have trouble remembering a lot of formulas, so they try to keep thenumber of formulas they have to know to a minimum. Can you learn just one formulathat will allow you to find probabilities for both independent and dependent events?Explain your reasoning. Sample answer: Just remember the formula fordependent events: P(A and B) � P(A) � P(B following A). When theevents are independent, P(B following A) � P(B), so the formula fordependent events simplifies to P(A and B) � P(A) � P(B), which is thecorrect formula for independent events.
P(Y)��P(Y) � P(B)
© Glencoe/McGraw-Hill 722 Glencoe Algebra 2
Conditional ProbabilitySuppose a pair of dice is thrown. It is known that the sum is greater thanseven. Find the probability that the dice match.
The probability of an event given the occurrence of another event is calledconditional probability. The conditional probability of event A, the dicematch, given event B, their sum is greater than seven, is denoted P(A/B).
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
12-412-4
There are 15 sums greater than seven andthere are 36 possible pairs altogether.
P(B) � �1356�
There are three matching pairs greaterthan seven.
P(A and B) � �336�
P(A/B) �
P(A/B) � or �15�
The conditional probability is �15�.
A card is drawn from a standard deck of 52 and is found to be red.Given that event, find each of the following probabilities.
1. P(heart) 2. P(ace) 3. P(face card)
4. P(jack or ten) 5. P(six of spades) 6. P(six of hearts)
A sports survey taken at Stirers High School shows that 48% of therespondents liked soccer, 66% liked basketball, and 38% liked hockey.Also, 30% liked soccer and basketball, 22% liked basketball and hockeyand 28% liked soccer and hockey. Finally, 12% liked all three sports.Find each of the following probabilities.
7. The probability Meg likes soccer if she likes basketball.
8. The probability Biff likes basketball if he likes soccer.
9. The probability Muffy likes hockey if she likes basketball.
10. The probability Greg likes hockey and basketball if he likes soccer.
�336�
�
�1356�
P(A and B)��P(B)
Study Guide and InterventionAdding Probabilities
NAME ______________________________________________ DATE ____________ PERIOD _____
12-512-5
© Glencoe/McGraw-Hill 723 Glencoe Algebra 2
Less
on
12-
5
Mutually Exclusive Events Events that cannot occur at the same time are calledmutually exclusive events.
Probability of Mutually If two events, A and B, are mutually exclusive, thenExclusive Events P(A or B ) � P(A) � P(B ).
This formula can be extended to any number of mutually exclusive events.
To choose an afternoon activity, summer campers pull slips ofpaper out of a hat. Today there are 25 slips for a nature walk, 35 slips forswimming, and 30 slips for arts and crafts. What is the probability that a camperwill pull a slip for a nature walk or for swimming?These are mutually exclusive events. Note that there is a total of 90 slips.
P(nature walk or swimming) � P(nature walk) � P(swimming)
� �2950� � �
3950� or �
23�
The probability of a camper’s pulling out a slip for a nature walk or for swimming is �23�.
By the time one tent of 6 campers gets to the front of the line, thereare only 10 nature walk slips and 15 swimming slips left. What is the probabilitythat more than 4 of the 6 campers will choose a swimming slip?
P(more than 4 swimmers) � P(5 swimmers) � P(6 swimmers)
� �
� 0.2The probability of more than 4 of the campers swimming is about 0.2.
Find each probability.
1. A bag contains 45 dyed eggs: 15 yellow, 12 green, and 18 red. What is the probability ofselecting a green or a red egg? �
23
�
2. The letters from the words LOVE and LIVE are placed on cards and put in a box. Whatis the probability of selecting an L or an O from the box? �
38
�
3. A pair of dice is rolled, and the two numbers are added. What is the probability that thesum is either a 5 or a 7? �
158� or about 0.28
4. A bowl has 10 whole wheat crackers, 16 sesame crackers, and 14 rye crisps. If a personpicks a cracker at random, what is the probability of picking either a sesame cracker ora rye crisp? �
34
�
5. An art box contains 12 colored pencils and 20 pastels. If 5 drawing implements are chosenat random, what is the probability that at least 4 of them are pastels? about 0.37
C(10, 0) � C(15, 6)���C(25, 6)
C(10, 1) � C(15, 5)���C(25, 6)
Example 1Example 1
Example 2Example 2
ExercisesExercises
© Glencoe/McGraw-Hill 724 Glencoe Algebra 2
Inclusive Events
Probability of Inclusive Events If two events, A and B, are inclusive, P(A or B ) � P(A) � P(B ) � P(A and B ).
What is the probability of drawing a face card or a black card froma standard deck of cards?The two events are inclusive, since a card can be both a face card and a black card.
P(face card or black card) � P(face card) � P(black card) � P(black face card)
� �133� � �
12� � �2
36�
� �183� or about 0.62
The probability of drawing either a face card or a black card is about 0.62
Find each probability.
1. What is the probability of drawing a red card or an ace from a standard deck of cards?
�173� or about 0.54
2. Three cards are selected from a standard deck of 52 cards. What is the probability ofselecting a king, a queen, or a red card?
�1256� or about 0.58
3. The letters of the alphabet are placed in a bag. What is the probability of selecting avowel or one of the letters from the word QUIZ?
�276� or about 0.27
4. A pair of dice is rolled. What is the probability that the sum is odd or a multiple of 3?
�171� or about 0.64
5. The Venn diagram at the right shows the number of juniors on varsity sports teams at Elmwood High School.Some athletes are on varsity teams for one season only,some athletes for two seasons, and some for all threeseasons. If a varsity athlete is chosen at random from the junior class, what is the probability that he or she plays a fall or winter sport? �
1136�
Winter
Juniors Playing Varsity Sports
Spring
Fall5
6
8 3
54 1
Study Guide and Intervention (continued)
Adding Probabilities
NAME ______________________________________________ DATE ____________ PERIOD _____
12-512-5
ExampleExample
ExercisesExercises
Skills PracticeAdding Probabilities
NAME ______________________________________________ DATE ____________ PERIOD _____
12-512-5
© Glencoe/McGraw-Hill 725 Glencoe Algebra 2
Less
on
12-
5
Eli has 10 baseball cards of 10 different players in his pocket. Three players arepitchers, 5 are outfielders, and 2 are catchers. If Eli randomly selects a card totrade, find each probability.
1. P(pitcher or outfielder) �45
� 2. P(pitcher or catcher) �12
� 3. P(outfielder or catcher) �170�
A die is rolled. Find each probability.
4. P(5 or 6) �13
� 5. P(at least a 3) �23
� 6. P(less than 4) �12
�
Determine whether the events are mutually exclusive or inclusive. Then find theprobability.
7. A die is rolled. What is the probability of rolling a 3 or a 4? mutually exclusive; �13
�
8. A die is rolled. What is the probability of rolling an even number or a 4? inclusive; �12
�
9. A card is drawn from a standard deck of cards. What is the probability of drawing a kingor a queen? mutually exclusive; �
123�
10. A card is drawn from a standard deck of cards. What is the probability of drawing a jackor a heart? inclusive; �
143�
11. The sophomore class is selling Mother’s Day plants to raise money. Susan’s prize forbeing the top seller of plants is a choice of a book, a CD, or a video. She can choose from6 books, 3 CDs, and 5 videos. What is the probability that Susan selects a book or a CD?
mutually exclusive; �194�
A spinner numbered 1�10 is spun. Find each probability.
12. P(less than 5 or even) �170� 13. P(even or odd) 1 14. P(prime or even) �
45
�
Two cards are drawn from a standard deck of cards. Find each probability.
15. P(both red or both black) �2551� 16. P(both aces or both red) �
25251
�
17. P(both 2s or both less than 5) �21211
� 18. P(both black or both less than 5) �168683
�
For Exercises 19 and 20, use the Venn diagram that shows the number of participants in two different kinds of aerobic exercise classes that are offered at a health club. Determine each probability if a person is selected at random from the participants.
19. P(step aerobics or jazzercise, but not both) �4692�
20. P(step aerobics and jazzercise) �1632�
JazzerciseStep
Aerobics
2722
13
© Glencoe/McGraw-Hill 726 Glencoe Algebra 2
An urn contains 7 white marbles and 5 blue marbles. Four marbles are selectedwithout replacement. Find each probability.
1. P(4 white or 4 blue) �989� 2. P(exactly 3 white) �
3959� 3. P(at least 3 white) �
1343�
4. P(fewer than 3 white) �1393� 5. P(3 white or 3 blue) �
4999� 6. P(no white or no blue) �
989�
Jason and Maria are playing a board game in which three dice are tossed todetermine a player’s move. Find each probability.
7. P(two 5s) �752� 8. P(three 5s) �
2116� 9. P(at least two 5s) �
227�
10. P(no 5s) �122156
� 11. P(one 5) �2752� 12. P(one 5 or two 5s) �
152�
Determine whether the events are mutually exclusive or inclusive. Then find theprobability.
13. A clerk chooses 4 CD players at random for floor displays from a shipment of 24 CD players.If 15 of the players have a blue case and the rest have a red case, what is the probability ofchoosing 4 players with a blue case or 4 players with a red case? mutual. exclus.; �
57016
�
14. A department store employs 28 high school students, all juniors and seniors. Six of the12 seniors are females and 12 of the juniors are males. One student employee is chosenat random. What is the probability of selecting a senior or a female? inclusive; �
47
�
15. A restaurant has 5 pieces of apple pie, 4 pieces of chocolate cream pie, and 3 pieces ofblueberry pie. If Janine selects a piece of pie at random for dessert, what is theprobability that she selects either apple or chocolate cream? mutually exclusive; �
34
�
16. At a statewide meeting, there are 20 school superintendents, 13 principals, and 6 assistantprincipals. If one of these people is chosen at random, what is the probability that he orshe is either a principal or an assistant principal? mutually exclusive; �
1399�
17. An airline has one bank of 13 telephones at a reservations office. Of the 13 operators whowork there, 8 take reservations for domestic flights and 5 take reservations for internationalflights. Seven of the operators taking domestic reservations and 3 of the operators takinginternational reservations are female. If an operator is chosen at random, what is theprobability that the person chosen takes domestic reservations or is a male?
inclusive; �1103�
18. MUSIC Forty senior citizens were surveyed about their music preferences. The results are displayed in the Venndiagram. If a senior citizen from the survey group isselected at random, what is the probability that he or she likes only country and western music? What is theprobability that he or she likes classical and/or country,but not 1940’s pop?�230�; �
25
�
Countryand
Western
1940’s Pop
Classical
6
9
3 7
65 4
Practice (Average)
Adding Probabilities
NAME ______________________________________________ DATE ____________ PERIOD _____
12-512-5
Reading to Learn MathematicsAdding Probabilities
NAME ______________________________________________ DATE ____________ PERIOD _____
12-512-5
© Glencoe/McGraw-Hill 727 Glencoe Algebra 2
Less
on
12-
5
Pre-Activity How does probability apply to your personal habits?
Read the introduction to Lesson 12-5 at the top of page 658 in your textbook.
Why do the percentages shown on the bar graph add up to more than100%? Sample answer: Many people do more than one of thelisted bedtime rituals.
Reading the Lesson
1. Indicate whether the events in each pair are inclusive or mutually exclusive.
a. Q: drawing a queen from a standard deck of cardsD: drawing a diamond from a standard deck of cards inclusive
b. J: drawing a jack from a standard deck of cardsK: drawing a king from a standard deck of cards mutually exclusive
2. Marla took a quiz on this lesson that contained the following problem.Each of the integers from 1 through 25 is written on a slip of paper and placed in anenvelope. If one slip is drawn at random, what is the probability that it is odd or amultiple of 5?Here is Marla’s work.
P(odd) � �1235� P(multiple of 5) � �2
55� or �
15�
P(odd or multiple of 5) � P(odd) � P(multiple of 5)
� �1235� � �2
55� � �
1285�
a. Why is Marla’s work incorrect? Sample answer: Marla used the formula formutually exclusive events, but the events are inclusive. She shoulduse the formula for inclusive events so that the odd multiples of 5 willnot be counted twice.
b. Show the corrected work.
P(odd or multiple of 5) � P(odd) � P(multiple of 5) � P(odd multiple of 5)
� �1235� � �
255� � �
235� � �
1255� � �
35
�
Helping You Remember
3. Some students have trouble remembering a lot of formulas, so they try to keep thenumber of formulas they have to know to a minimum. Can you learn just one formulathat will allow you to find probabilities for both mutually exclusive and inclusive events?Explain your reasoning. Sample answer: Just remember the formula forinclusive events: P(A or B) � P(A) � P(B) � P(A and B). When theevents are mutually exclusive, P(A and B) � 0, so the formula forinclusive events simplifies to P(A and B) � P(A) � P(B), which is thecorrect formula for mutually exclusive events.
© Glencoe/McGraw-Hill 728 Glencoe Algebra 2
Probability and Tic-Tac-ToeWhat would be the chances of winning at tic-tac-toe if it were turned into agame of pure chance? To find out, the nine cells of the tic-tac-toe board arenumbered from 1 to 9 and nine chips (also numbered from 1 to 9) are putinto a bag. Player A draws a chip at random and enters an X in thecorresponding cell. Player B does the same and enters an O.
To solve the problem, assume that both players draw all their chips withoutlooking and all X and O entries are made at the same time. There are fourpossible outcomes: a draw, A wins, B wins, and either A or B can win.
There are 16 arrangements that result in a draw. Reflections and rotationsmust be counted as shown below.
o x o x o x o o xx o x 4 o o x 4 x x o 8x o x x x o o x x
There are 36 arrangements in which either player may win because bothplayers have winning triples.
x x x x x x x o x x x x x x x x x oo o o 4 x o x 4 x x x 4 x x o 8 o o o 8 x x x 8x o x o o o o o o o o o x x o o o o
In these 36 cases, A’s chances of winning are �1430�.
1. Find the 12 arrangements in which B wins and A cannot.
2. Below are 12 of the arrangements in which A wins and B cannot. Writethe numbers to show the reflections and rotations for each arrangement.What is the total number?
o x o x o x x x x x x x x o o x o ox x x o x o x o o o x o x x x x x oo x o x o x x o o o x o o o x o o x
x x o x x x x x x x x x x o o x x oo x x o x o x o o x o o x x x o x oo o x o o x o x o o o x o x o x o x
3. There are �(59!4!!)� different and equally probable
distributions. Complete the chart to find the probability for a draw or for A or B to win.
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
12-512-5
Draw: �
A wins: � �1430�� � �
B wins: � �
36�126
16�126
Study Guide and InterventionStatistical Measures
NAME ______________________________________________ DATE ____________ PERIOD _____
12-612-6
© Glencoe/McGraw-Hill 729 Glencoe Algebra 2
Less
on
12-
6Measures of Central Tendency
Use When
Measures of mean the data are spread out and you want an average of values
Central Tendency median the data contain outliers
mode the data are tightly clustered around one or two values
Find the mean, median, and mode of the following set of data:{42, 39, 35, 40, 38, 35, 45}.To find the mean, add the values and divide by the number of values.
mean � � 39.14.
To find the median, arrange the values in ascending or descending order and choose themiddle value. (If there is an even number of values, find the mean of the two middle values.)In this case, the median is 39.To find the mode, take the most common value. In this case, the mode is 35.
Find the mean, median, and mode of each set of data. Round to the nearesthundredth, if necessary.
1. {238, 261, 245, 249, 255, 262, 241, 245} 249.5; 247; 245
2. {9, 13, 8, 10, 11, 9, 12, 16, 10, 9} 10.7; 10; 9
3. {120, 108, 145, 129, 102, 132, 134, 118, 108, 142} 123.8; 124.5; 108
4. {68, 54, 73, 58, 63, 72, 65, 70, 61} 64.89; 65; no mode
5. {34, 49, 42, 38, 40, 45, 34, 28, 43, 30} 38.3; 39; 34
6. The table at the right shows the populations of the six New England capitals. Which would be themost appropriate measure of central tendency to represent the data? Explain why and find that value.Source: www.factfinder.census.gov There is no mode. Thepopulation of Boston is an outlier and would raise the mean too high. The median,79,500, would be the best choice.
CityPopulation (roundedto the nearest 1000)
Augusta, ME 19,000
Boston, MA 589,000
Concord, NH 37,000
Hartford, CT 122,000
Montpelier, VT 8,000
Providence, RI 174,000
42 � 39 � 35 � 40 � 38 � 35 � 45�����7
ExampleExample
ExercisesExercises
© Glencoe/McGraw-Hill 730 Glencoe Algebra 2
Measures of Variation The range and the standard deviation measure howscattered a set of data is.
Standard If a set of data consists of the n values x1, x2, …, xn and has mean x�, then the standard deviation
Deviationis given by � � ���.
The square of the standard deviation is called the variance.
Find the variance and standard deviation of the data set {10, 9, 6, 9, 18, 4, 8, 20}.Step 1 Find the mean.
x� � � 10.5
Step 2 Find the variance.
�2 � Standard variance formula
�
� or 27.5
Step 3 Find the standard deviation.� � �27.5�
� 5.2
The variance is 27.5 and the standard deviation is about 5.2.
Find the variance and standard deviation of each set of data. Round to thenearest tenth.
1. {100, 89, 112, 104, 96, 108, 93} 2. {62, 54, 49, 62, 48, 53, 50}58.5; 7.6 29.4; 5.4
3. {8, 9, 8, 8, 9, 7, 8, 9, 6} 4. {4.2, 5.0, 4.7, 4.5, 5.2, 4.8, 4.6, 5.1}0.9; 0.9 0.1; 0.3
5. The table at the right lists the prices of ten brands of breakfast cereal. What is the standard deviation of the values to the nearest penny? $0.33
Price of 10 Brandsof Breakfast Cereal
$2.29 $3.19
$3.39 $2.79
$2.99 $3.09
$3.19 $2.59
$2.79 $3.29
220�8
(10 � 10.5)2 � (9 � 10.5)2 � … � (20 � 10.5)2������8
(x1 � x�)2 � (x2 � x�)2 � … � (xn � x�)2�����n
10 � 9 � 6 � 9 � 18 � 4 � 8 � 20�����8
(x1 � x�)2 � (x2 � x�)2 � … � (xn � x�)2
�����n
Study Guide and Intervention (continued)
Statistical Measures
NAME ______________________________________________ DATE ____________ PERIOD _____
12-612-6
ExampleExample
ExercisesExercises
Skills PracticeStatistical Measures
NAME ______________________________________________ DATE ____________ PERIOD _____
12-612-6
© Glencoe/McGraw-Hill 731 Glencoe Algebra 2
Less
on
12-
6Find the variance and standard deviation of each set of data to the nearest tenth.
1. {32, 41, 35, 35, 46, 42} 23.6, 4.9
2. {13, 62, 77, 24, 38, 19, 88} 763.8, 27.6
3. {89, 99, 42, 16, 42, 71, 16} 959.1, 31.0
4. {450, 400, 625, 225, 300, 750, 650, 625} 30,537.1; 174.7
5. {17, 23, 65, 94, 33, 33, 33, 8, 57, 75, 44, 12, 11, 68, 39} 630.7, 25.1
6. {7.2, 3.1, 3.8, 9.5, 8.3, 8.4} 5.8, 2.4
7. {1.5, 2.5, 3.5, 4.5, 4.5, 5.5, 6.5, 7.5} 3.5, 1.9
For Exercises 8 and 9, use the table that shows the profit in billions of dollarsreported by U.S. manufacturers for the first quarter of the years from 1997through 2001.
Source: U. S. Census Bureau
8. Find the mean and median of the data to the nearest tenth. $64.3 billion, $61.4 billion
9. Which measure of central tendency best represents the data? Explain.The median is more representative because the value 45.3 is not close tothe other data points, and it lowers the mean.
For Exercises 10 and 11, use the table that shows the percent of fourth gradestudents reading at or above the proficiency level in a nationally-administeredreading assessment.
Source: National Center for Education Statistics
10. Find the mean, median, and standard deviation of the data to the nearest tenth.30.5%, 30.5%, 1.1
11. What do the statistics from Exercise 11 tell you about the data?Sample answer: Since the median and mean are equal and the standarddeviation is small, the percent of students reading at or above theproficiency level has not varied much from 1992 to 2000.
Year 1992 1994 1998 2000
Percent at or above proficiency level
29% 30% 31% 32%
Year 1997 1998 1999 2000 2001
Seasonally-Adjusted Profit ($ billions)
$61.4 $75.6 $60.9 $78.5 $45.3
© Glencoe/McGraw-Hill 732 Glencoe Algebra 2
Find the variance and standard deviation of each set of data to the nearest tenth.
1. {47, 61, 93, 22, 82, 22, 37} 2. {10, 10, 54, 39, 96, 91, 91, 18}673.1, 25.9 1228.6, 35.1
3. {1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5} 4. {1100, 725, 850, 335, 700, 800, 950}1.6, 1.2 49,150.0; 221.7
5. {3.4, 7.1, 8.5, 5.1, 4.7, 6.3, 9.9, 8.4, 3.6} 6. {2.8, 0.5, 1.9, 0.8, 1.9, 1.5, 3.3, 2.6, 0.7, 2.5}4.7, 2.2 0.8, 0.9
7. HEALTH CARE Eight physicians with 15 patients on a hospital floor see these patientsan average of 18 minutes a day. The 22 nurses on the same floor see the patients anaverage of 3 hours a day. As a hospital administrator, would you quote the mean,median, or mode as an indicator of the amount of daily medical attention the patients onthis floor receive? Explain. Either the median or the mode; they are equal andhigher than the mean, which is lowered by the smaller amount of timethe physicians spend with the patients.
For Exercises 8–10, use the frequency table that shows the percent of public schoolteachers in the U. S. in 1999 who used computers or theInternet at school for variousadministrative and teachingactivities.
8. Find the mean, median, and modeof the data. 17.75%, 12%, 8%
9. Suppose you believe teachers usecomputers or the Internet tooinfrequently. Which measure would you quote as the “average?” Source: National Assessment of Educational Progress
Explain. Mode; it is lowest.
10. Suppose you believe teachers use computers or the Internet too often. Which measurewould you quote as the “average?” Explain. Mean; it is highest.
For Exercises 11 and 12, use the frequency table that shows the number of games played by 24 American League baseball players between opening day, 2001 andSeptember 8, 2001.
11. Find the mean, median, mode, and standard deviation of thenumber of games played to the nearest tenth.138.2, 138; 138, 2.0
12. For how many players is the number of games within onestandard deviation of the mean? 14
Source: Major League Baseball
No. of Games Frequency
141 4
140 3
139 4
138 5
137 2
136 3
135 3
Percent Using Activity Computer
or Internet
Create instructional materials 39
Administrative record keeping 34
Communicate with colleagues 23
Gather information for planning lessons 16
Multimedia classroom presentations 8
Access research and best practices for teaching 8
Communicate with parents or students 8
Access model lesson plans 6
Practice (Average)
Statistical Measures
NAME ______________________________________________ DATE ____________ PERIOD _____
12-612-6
Reading to Learn MathematicsStatistical Measures
NAME ______________________________________________ DATE ____________ PERIOD _____
12-612-6
© Glencoe/McGraw-Hill 733 Glencoe Algebra 2
Less
on
12-
6Pre-Activity What statistics should a teacher tell the class after a test?
Read the introduction to Lesson 12-6 at the top of page 664 in your textbook.
There is more than one way to give an “average” score for this test. Threemeasures of central tendency for these scores are 94, 76.5 and 73.9. Can youtell which of these is the mean, the median, and the mode without doing anycalculations? Explain your answer.
Sample answer: Yes. The mode must be one of the scores, soit must be an integer. The median must be either one of thescores or halfway between two of the scores, so it must be aninteger or a decimal ending with .5. Therefore, 94 is the mode,76.5 is the median, and 73.9 is the mean.
Reading the Lesson
1. Match each measure with one of the six descriptions of how to find measures of centraltendency and variation.
a. median vi b. mode i c. range iv
d. variance iii e. mean ii f. standard deviation v
i. Find the most commonly occurring values or values in a set of data.
ii. Add the data and divide by the number of items.
iii. Find the mean of the squares of the differences between each value in the set of dataand the mean.
iv. Find the difference between the largest and smallest values in the set of data.
v. Take the positive square root of the variance.
vi. If there is an odd number of items in a set of data, take the middle one. If there is aneven number of items, add the two middle items and divide by 2.
Helping You Remember
2. It is usually easier to remember a complicated procedure if you break it down into steps.Write the procedure for finding the standard deviation for a set of data in a series ofbrief, numbered steps.
Sample answer: 1. Find the mean. 2. Find the difference between each value and the mean. 3. Square each difference. 4. Find the mean of the squares. 5. Take the positive square root.
© Glencoe/McGraw-Hill 734 Glencoe Algebra 2
Probabilities in GeneticsGenes are the units which transmit hereditary traits. The possible formswhich a gene may take, dominant and recessive, are called alleles. Aparticular trait is determined by two alleles, one from the female parent andone from the male parent. If an organism has the trait which is dominant, itmay have either two dominant alleles or one dominant and one recessiveallele. If the organism has the trait which is recessive, it must have tworecessive alleles.
Consider a plant in which tall stems, T, are dominant toshort stems, t. What is the probability of obtaining a long-stemmedplant if two long-stemmed plants both with the genetic formula Ttare crossed?
A Punnett square is a chart used to determine the possible combinations of characteristics among offspring.
3 tall-stemmed� 1 short-stemmed
4 total
Thus, the probability is �34�.
In a certain plant, red flowers, R, are dominant to white flowers, r.If a white-flowered plant, rr is crossed with a red-flowered plant, Rr,find the probability of each of the following.
1. white-flowered plant �12
� 2. red-flowered plant �12
�
In a certain plant, tall, T, is dominant to short, t, and green pods, G,are dominant to yellow pods, g. Plants with the genetic formulasTtGg and TTGg are crossed. Find the probability of each of thefollowing.
3. tall plant with green pods �34
� 4. tall plant with yellow pods �14
�
TT Tt
T t
Tt
T
t tt
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
12-612-6
ExampleExample
Study Guide and InterventionThe Normal Distribution
NAME ______________________________________________ DATE ____________ PERIOD _____
12-712-7
© Glencoe/McGraw-Hill 735 Glencoe Algebra 2
Less
on
12-
7
Normal and Skewed Distributions A continuous probability distribution isrepresented by a curve.
Types of
Normal Positively Skewed Negatively Skewed
ContinuousDistributions
Determine whether the data below appear to be positively skewed,negatively skewed, or normally distributed.{100, 120, 110, 100, 110, 80, 100, 90, 100, 120, 100, 90, 110, 100, 90, 80, 100, 90}Make a frequency table for the data.
Then use the data to make a histogram.Since the histogram is roughly symmetric, the data appear to be normally distributed.
Determine whether the data in each table appear to be positively skewed,negatively skewed, or normally distributed. Make a histogram of the data.
1. {27, 24, 29, 25, 27, 22, 24, 25, 29, 24, 25, 22, 27, 24, 22, 25, 24, 22}positively skewed
2.
normally distributed
3. negatively skewed
�100 101–120
121–140
141–160
161–180
181–200
200�
12
10
8
6
4
2
Freq
uen
cy
Thousands of Dollars
Housing Price No. of Houses Sold
less than $100,000 0
$100,00�$120,000 1
$121,00�$140,000 3
$141,00�$160,000 7
$161,00�$180,000 8
$181,00�$200,000 6
over $200,000 12
104
8
6
4
2Freq
uen
cy
5 6 7 8 9
Shoe Size 4 5 6 7 8 9 10
No. of Students 1 2 4 8 5 1 2
22
6
4
2Freq
uen
cy
24 25 27 29
Value 80 90 100 110 120
Frequency 2 4 7 3 2
80
6
4
2Freq
uen
cy
90 100 110 120
ExampleExample
ExercisesExercises
© Glencoe/McGraw-Hill 736 Glencoe Algebra 2
Use Normal Distributions
Normal Distribution Normal distributions have these properties.The graph is maximized at the mean.The mean, median, and mode are about equal.About 68% of the values are within one standard deviation of the mean.About 95% of the values are within two standard deviations of the mean.About 99% of the values are within three standard deviations of the mean.
The heights of players in a basketball league are normallydistributed with a mean of 6 feet 1 inch and a standard deviation of 2 inches.
a. What is the probability that a player selected at random will be shorter than 5 feet 9 inches?Draw a normal curve. Label the mean and the mean plus or minus multiples of the standard deviation.The value of 5 feet 9 inches is 2 standard deviations below the mean, so approximately 2.5% of the players will be shorter than 5 feet 9 inches.
b. If there are 240 players in the league, about how many players are taller than 6feet 3 inches?The value of 6 feet 3 inches is one standard deviation above the mean. Approximately16% of the players will be taller than this height.240 � 0.16 � 38About 38 of the players are taller than 6 feet 3 inches.
EGG PRODUCTION The number of eggs laid per year by a particular breed ofchicken is normally distributed with a mean of 225 and a standard deviation of 10 eggs.
1. About what percent of the chickens will lay between 215 and 235 eggs per year? 68%
2. In a flock of 400 chickens, about how many would you expect to lay more than 245 eggsper year? 10 chickens
MANUFACTURING The diameter of bolts produced by a manufacturing plant isnormally distributed with a mean of 18 mm and a standard deviation of 0.2 mm.
3. What percent of bolts coming off of the assembly line have a diameter greater than 18.4 mm? 2.5%
4. What percent have a diameter between 17.8 and 18.2 mm? 68%
5'7" 5'9" 5'11" 6'1" 6'3" 6'5" 6'7"
�3
mean
�2 � � �2 �3
Study Guide and Intervention (continued)
The Normal Distribution
NAME ______________________________________________ DATE ____________ PERIOD _____
12-712-7
ExampleExample
ExercisesExercises
Skills PracticeThe Normal Distribution
NAME ______________________________________________ DATE ____________ PERIOD _____
12-712-7
© Glencoe/McGraw-Hill 737 Glencoe Algebra 2
Less
on
12-
7
Determine whether the data in each table appear to be positively skewed,negatively skewed, or normally distributed.
1. 2.
normally distributed negatively skewed
For Exercises 3 and 4, use the frequency table that shows the average number of days patients spent on thesurgical ward of a hospital last year.
3. Make a histogram of the data.
4. Do the data appear to be positivelyskewed, negatively skewed, or normally distributed? Explain.Positively skewed; thehistogram is high at the left and has a tail to the right.
DELIVERY For Exercises 5–7, use the following information.The time it takes a bicycle courier to deliver a parcel to his farthest customer is normallydistributed with a mean of 40 minutes and a standard deviation of 4 minutes.
5. About what percent of the courier’s trips to this customer take between 36 and 44 minutes?68%
6. About what percent of the courier’s trips to this customer take between 40 and 48 minutes?47.5%
7. About what percent of the courier’s trips to this customer take less than 32 minutes? 2.5%
TESTING For Exercises 8–10, use the following information.The average time it takes sophomores to complete a math test is normally distributed witha mean of 63.3 minutes and a standard deviation of 12.3 minutes.
8. About what percent of the sophomores take more than 75.6 minutes to complete the test?16%
9. About what percent of the sophomores take between 51 and 63.3 minutes? 34%
10. About what percent of the sophomores take less than 63.3 minutes to complete the test?50%
0–3 4–7 8–11 12–15 16�
2018161412108642
Freq
uen
cy
Days
Patient Stays
Days Number of Patients
0–3 5
4–7 18
8–11 11
12–15 9
16� 6
Speeches Given Political Candidates
0–5 1
6–11 2
12–17 3
18–23 8
24–29 8
Miles Run Track Team Members
0–4 3
5–9 4
10–14 7
15–19 5
20–23 2
© Glencoe/McGraw-Hill 738 Glencoe Algebra 2
Determine whether the data in each table appear to be positively skewed,negatively skewed, or normally distributed.
1. 2.
normally distributed
negatively skewed
For Exercises 3 and 4, use the frequency table that shows the number of hours worked per week by 100 high school seniors.
3. Make a histogram of the data.
4. Do the data appear to be positivelyskewed, negatively skewed, or normally distributed? Explain.Positively skewed; thehistogram is high at the left and has a tail to the right.
TESTING For Exercises 5–10, use the following information.The scores on a test administered to prospective employees are normally distributed with amean of 100 and a standard deviation of 15.
5. About what percent of the scores are between 70 and 130? 95%
6. About what percent of the scores are between 85 and 130? 81.5%
7. About what percent of the scores are over 115? 16%
8. About what percent of the scores are lower than 85 or higher than 115? 32%
9. If 80 people take the test, how many would you expect to score higher than 130? 2
10. If 75 people take the test, how many would you expect to score lower than 85? 12
11. TEMPERATURE The daily July surface temperature of a lake at a resort has a mean of82� and a standard deviation of 4.2�. If you prefer to swim when the temperature is atleast 77.8�, about what percent of the days does the temperature meet your preference?84%
0–8 9–17 18–25 26�
605040302010Fr
equ
ency
Hours
Weekly Work Hours
Hours Number of Students
0–8 30
9–17 45
18–25 20
26� 5
Average Age of High School Principals
Age in Years Number
31–35 3
36–40 8
41–45 15
46–50 32
51–55 40
56–60 38
60� 4
Time Spent at a Museum Exhibit
Minutes Frequency
0–25 27
26–50 46
51–75 89
75–100 57
100� 24
Practice (Average)
The Normal Distribution
NAME ______________________________________________ DATE ____________ PERIOD _____
12-712-7
Reading to Learn MathematicsThe Normal Distribution
NAME ______________________________________________ DATE ____________ PERIOD _____
12-712-7
© Glencoe/McGraw-Hill 739 Glencoe Algebra 2
Less
on
12-
7
Pre-Activity How are the heights of professional athletes distributed?
Read the introduction to Lesson 12-7 at the top of page 671 in your textbook.
There were 53 players on the team and the mean height was approximately73.6. About what fraction of the players’ heights are between 72 and 75,inclusive? Sample answer: about �
23
�
Reading the Lesson
1. Indicate whether each of the following statements is true or false.
a. In a continuous probability distribution, there is a finite number of possible outcomes. false
b. Every normal distribution can be represented by a bell curve. true
c. A distribution that is represented by a curve that is high at the left and has a tail tothe right is negatively skewed. false
d. A normal distribution is an example of a skewed distribution. false
2. Ms. Rose gave the same quiz to her two geometry classes. She recorded the following scores.
First-period class:
Fifth-period class:
In each class, 30 students took the quiz. The mean score for each class was 6.4. Whichset of scores has the greater standard deviation? (Answer this question without doingany calculations.) Explain your answer.
First period class; sample answer: The scores are more spread out fromthe mean than for the fifth period class.
Helping You Remember
3. Many students have trouble remembering how to determine if a curve represents adistribution that is positively skewed or negatively skewed. What is an easy way toremember this?
Sample answer: Follow the tail! If the tail is on the right (positivedirection), the distribution is positively skewed. If the tail is on the left(negative direction), the distribution is negatively skewed.
Score 0 1 2 3 4 5 6 7 8 9 10
Frequency 0 0 0 0 3 4 9 7 6 1 0
Score 0 1 2 3 4 5 6 7 8 9 10
Frequency 1 0 1 0 3 4 5 7 4 3 2
© Glencoe/McGraw-Hill 740 Glencoe Algebra 2
Street Networks: Finding All Possible RoutesA section of a city is laid out in square blocks. Going north from the intersection of First Avenue and First Street, the avenues are 1st, 2nd, 3rd, and so on. Going east, the streets are numbered in the same way.
Factorials can be used to find the number, r(e, n), of different routes between two intersections. The formula is shown below.
r(e, n) �
The number of streets going east is e; the number of avenues going north is n.
The following problems examine the possible routes from one location to another. Assume that you never use a route that is unnecessarily long.Assume that e 1 and n 1.
Solve each problem.
1. List all the possible routes from 1st Street and 1st Avenue to 4th Streetand 3rd Avenue. Use ordered pairs to show the routes, with streetnumbers first, and avenue numbers second. For example, each routestarts at (1, 1) and ends at (4, 3).
2. Use the formula to compute the number of routes from (1, 1) to (4, 3).There are 4 streets going east and 3 avenues going north.(3
3. Find the number of routes from 1st Street and 1st Avenue to 7th Streetand 6th Avenue.
�6!5
5!)!
� 462
[(e � 1) � (n � 1)]!���(e � 1)!(n � 1)!
6th Ave
5th Ave
4th Ave
3rd Ave
2nd Ave
1st Ave
1st S
t.
2nd
St.
3rd
St.
4th
St.
5th
St.
6th
St.
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
12-712-7
Study Guide and InterventionBinomial Experiments
NAME ______________________________________________ DATE ____________ PERIOD _____
12-812-8
© Glencoe/McGraw-Hill 741 Glencoe Algebra 2
Less
on
12-
8
Binomial Expansions For situations with only 2 possible outcomes, you can use theBinomial Theorem to find probabilities. The coefficients of terms in a binomial expansioncan be found by using combinations.
What is the probability that 3 coins show heads and 3 show tailswhen 6 coins are tossed?There are 2 possible outcomes that are equally likely: heads (H) and tails (T). The tosses of 6 coins are independent events. When (H � T)6 is expanded, the term containing H3T3,which represents 3 heads and 3 tails, is used to get the desired probability. By the BinomialTheorem the coefficient of H3T3 is C(6, 3).
P(3 heads, 3 tails) � �36!3!!� ��
12��3��
12��3 P(H) � �
12
� and P(T) � �12
�
� �2604�
� �156�
The probability of getting 3 heads and 3 tails is �156� or 0.3125.
Find each probability if a coin is tossed 8 times.
1. P(exactly 5 heads) 2. P(exactly 2 heads)
about 22% about 11%
3. P(even number of heads) 4. P(at least 6 heads)
50% about 14%
Mike guesses on all 10 questions of a true-false test. If the answers true and falseare evenly distributed, find each probability.
5. Mike gets exactly 8 correct answers. 6. Mike gets at most 3 correct answers.
or 0.044 or 0.172
7. A die is tossed 4 times. What is the probability of tossing exactly two sixes?
or 0.11625�
11�
45�
ExampleExample
ExercisesExercises
© Glencoe/McGraw-Hill 742 Glencoe Algebra 2
Binomial Experiments
A binomial experiment is possible if and only if all of these conditions occur.• There are exactly two outcomes for each trial.
Binomial Experiments • There is a fixed number of trials.• The trials are independent.• The probabilities for each trial are the same.
Suppose a coin is weighted so that the probability of getting heads inany one toss is 90%. What is the probability of getting exactly 7 heads in 8 tosses?
The probability of getting heads is �190�, and the probability of getting tails is �1
10�. There are
C(8, 7) ways to choose the 7 heads.
P(7 heads) � C(8, 7)� �7� �1
� 8 �
� 0.38
The probability of getting 7 heads in 8 tosses is about 38%.
1. BASKETBALL For any one foul shot, Derek has a probability of 0.72 of getting the shotin the basket. As part of a practice drill, he shoots 8 shots from the foul line.
a. What is the probability that he gets in exactly 6 foul shots? about 31%b. What is the probability that he gets in at least 6 foul shots? about 60%
2. SCHOOL A teacher is trying to decide whether to have 4 or 5 choices per question onher multiple choice test. She wants to prevent students who just guess from scoring wellon the test.
a. On a 5-question multiple-choice test with 4 choices per question, what is theprobability that a student can score at least 60% by guessing? 10.4%
b. What is the probability that a student can score at least 60% by guessing on a test ofthe same length with 5 choices per question? 5.8%
3. Julie rolls two dice and adds the two numbers.
a. What is the probability that the sum will be divisible by 3? �13
�
b. If she rolls the dice 5 times what is the chance that she will get exactly 3 sums thatare divisible by 3? about 16%
4. SKATING During practice a skater falls 15% of the time when practicing a triple axel.During one practice session he attempts 20 triple axels.
a. What is the probability that he will fall only once? about 14%b. What is the probability that he will fall 4 times? about 18%
97�108
1�10
9�10
Study Guide and Intervention (continued)
Binomial Experiments
NAME ______________________________________________ DATE ____________ PERIOD _____
12-812-8
ExampleExample
ExercisesExercises
Skills PracticeBinomial Experiments
NAME ______________________________________________ DATE ____________ PERIOD _____
12-812-8
© Glencoe/McGraw-Hill 743 Glencoe Algebra 2
Less
on
12-
8
Find each probability if a coin is tossed 4 times.
1. P(4 heads) �116� 2. P(0 heads) �
116�
3. P(exactly 3 heads) �14
� 4. P(exactly 2 heads) �38
�
5. P(exactly 1 head) �14
� 6. P(at least 3 heads) �156�
Find each probability if a die is rolled 3 times.
7. P(exactly one 2) �2752� 8. P(exactly two 2s) �
752�
9. P(exactly three 2s) �2116� 10. P(at most one 2) �
2257�
A town that presents a fireworks display during its July 4 celebration found the probability that a family with two or more children will watch the fireworks is �
35�.
If 5 of these families are selected at random, find each probability.
11. P(exactly 3 families watch the fireworks) 12. P(exactly 2 families watch the fireworks)
�261265
� �164245
�
13. P(exactly 5 families watch the fireworks) 14. P(no families watch the fireworks)
�3214235
� �331225�
15. P(at least 4 families watch the fireworks) 16. P(at most 1 family watches the fireworks)
�13015235
� �3217225
�
One section of a standardized English language test has 10 true/false questions.Find each probability when a student guesses at all ten questions.
17. P(exactly 8 correct) �140524� 18. P(exactly 2 correct) �
140524�
19. P(exactly half correct) �26536
� 20. P(all 10 correct) �10
124�
21. P(0 correct) �10
124� 22. P(at least 8 correct) �
1728�
© Glencoe/McGraw-Hill 744 Glencoe Algebra 2
Find each probability if a coin is tossed 6 times.
1. P(exactly 3 tails) �156� 2. P(exactly 5 tails) �
332�
3. P(0 tails) �614� 4. P(at least 4 heads) �
1312�
5. P(at least 4 tails) �1312� 6. P(at most 2 tails) �
1312�
The probability of Chris making a free throw is �23�. If she shoots 5 times, find each
probability.
7. P(all missed) �2143� 8. P(all made) �
23423
�
9. P(exactly 2 made) �24403
� 10. P(exactly 1 missed) �28403
�
11. P(at least 3 made) �6841� 12. P(at most 2 made) �
1871�
When Tarin and Sam play a certain board game, the probability that Tarin will win a game is �
34�. If they play 5 games, find each probability.
13. P(Sam wins only once) �1400254
� 14. P(Tarin wins exactly twice) �54152
�
15. P(Sam wins exactly 3 games) �54152
� 16. P(Sam wins at least 1 game) �1708214
�
17. P(Tarin wins at least 3 games) �455192
� 18. P(Tarin wins at most 2 games) �55132
�
19. SAFETY In August 2001, the American Automobile Association reported that 73% ofAmericans use seat belts. In a random selection of 10 Americans in 2001, what is theprobability that exactly half of them use seat belts? Source: AAA about 7.5%
HEALTH For Exercises 20 and 21, use the following information.In 2001, the American Heart Association reported that 50 percent of the Americans whoreceive heart transplants are ages 50–64 and 20 percent are ages 35–49. Source: American Heart Association
20. In a randomly selected group of 10 heart transplant recipients, what is the probabilitythat at least 8 of them are ages 50–64? �
1728�
21. In a randomly selected group of 5 heart transplant recipients, what is the probabilitythat 2 of them are ages 35–49? �
162285
�
Practice (Average)
Binomial Experiments
NAME ______________________________________________ DATE ____________ PERIOD _____
12-812-8
Reading to Learn MathematicsBinomial Experiments
NAME ______________________________________________ DATE ____________ PERIOD _____
12-812-8
© Glencoe/McGraw-Hill 745 Glencoe Algebra 2
Less
on
12-
8
Pre-Activity How can you determine whether guessing is worth it?
Read the introduction to Lesson 12-8 at the top of page 676 in your textbook.
Suppose you are taking a 50-question multiple-choice test in which thereare 5 answer choices for each question. You are told that no points will bededucted for wrong answers. Should you guess the answers to the questionsyou do not know? Explain your reasoning. Sample answer: Yes; the probability of guessing the right answer to a question is �
15
�, so you have a chance to get some points by guessing, and youhave nothing to lose.
Reading the Lesson1. Indicate whether each of the following is a binomial experiment or not a binomial
experiment. If the experiment is not a binomial experiment, explain why.
a. A fair coin is tossed 10 times and “heads” or “tails” is recorded each time. binomialexperiment
b. A pair of dice is thrown 5 times and the sum of the numbers that come up is recordedeach time. Not a binomial experiment; there are more than two possibleoutcomes for each trial.
c. There are 5 red marbles and 6 blue marbles in a bag. One marble is drawn from thebag and its color recorded. The marble is not put back in the bag. A second marble isdrawn and its color recorded. Not a binomial experiment; the trials are notindependent (or, the probabilities for the two trials are not the same).
d. There are 5 red marbles and 6 blue marbles in a bag. One marble is drawn from thebag and its color recorded. The marble is put back in the bag. A second marble isdrawn and its color recorded. binomial experiment
2. Len randomly guesses the answers to all 6 multiple-choice questions on his chemistrytest. Each question has 5 choices. Which of the following expressions gives theprobability that he will get at least 4 of the answers correct? B
A. P(6, 4)��15��4��
45��2
� P(6, 5)��15��5��
45��1
� P(6, 6)��15��6��
45��0
B. C(6, 4)��15��4��
45��2
� C(6, 5)��15��5��
45��1
� C(6, 6)��15��6��
45��0
C. C(6, 4)��15��2��
45��4
� C(6, 5)��15��1��
45��5
� C(6, 6)��15��0��
45��6
Helping You Remember3. Some students have trouble remembering how to calculate binomial probabilities. What is
an easy way to remember which numbers to put into an expression like C(6, 4)��15��2��
45��4?
Sample answer: The binomial coefficient is C(n, r), where n is thenumber of trials and r is the number of successes. The probability ofsuccess is raised to the r th power and the probability of failure is raisedto the
© Glencoe/McGraw-Hill 746 Glencoe Algebra 2
Misuses of StatisticsStatistics can be misleading. Graphs for a set of data can look very differentfrom one another. Compare the following graphs.
Notice that the two graphs show the same data, but the spacing in thevertical and horizontal scales differs. Scales can be cramped or spread out tomake a graph that gives a certain impression. Which graph would you use togive the impression that the unemployment rate dropped dramatically from1990 to 2000?
Suppose that a car company claims, “75% of people surveyed say that our caris better than the competition.” If four people were asked which car theypreferred and 75% agreed, how many people thought that Our Car wasbetter?
The advertisement was misleading in other ways as well. For example, whowas surveyed—were the people company employees, or impartial buyers?
Suppose an advertiser claims that 90% of all of one brand of car soldin the last 10 years are still on the road.
1. If 10,000 cars were sold, how many are still on the road? 9,000
2. If 1000 cars were sold, how many are still on the road? 900
3. Find an example to show how you think averages could be used in amisleading way. See students’ work.
4. A survey of a large sample of people who own small computers revealedthat 85% of the people thought the instruction manuals should be betterwritten. A manufacturer of small computers claimed that it surveyedmany of the same people and found that all of them liked their manuals.Discuss the possible discrepancy in the results. See students’ work.
U.S. Unemployment Rate
Year
Perc
ent
0 ’90 ’92 ’94 ’96 ’02’98 ’00
8
7
6
5
4
Source: U.S. Department of Labor
U.S. Unemployment Rate
Year
Perc
ent
0 ’90 ’92 ’94 ’96 ’02’98 ’00’91 ’93 ’95 ’97 ’99 ’01
87654
Source: U.S. Department of Labor
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
12-812-8
Study Guide and InterventionSampling and Error
NAME ______________________________________________ DATE ____________ PERIOD _____
12-912-9
© Glencoe/McGraw-Hill 747 Glencoe Algebra 2
Less
on
12-
9
Bias A sample of size n is random (or unbiased) when every possible sample of size n hasan equal chance of being selected. If a sample is biased, then information obtained from itmay not be reliable.
To find out how people in the U.S. feel about mass transit, people ata commuter train station are asked their opinion. Does this situation represent arandom sample?No; the sample includes only people who actually use a mass-transit facility. The sampledoes not include people who ride bikes, drive cars, or walk.
Determine whether each situation would produce a random sample. Write yes orno and explain your answer.
1. asking people in Phoenix, Arizona, about rainfall to determine the average rainfall forthe United States No; it rains less in Phoenix than most places in the U.S.
2. obtaining the names of tree types in North America by surveying all of the U.S. NationalForests Yes; there are National Forests in about every state in the U.S.
3. surveying every tenth person who enters the mall to find out about music preferences inthat part of the country Yes; mall customers should be fairly representativein terms of music tastes.
4. interviewing country club members to determine the average number of televisions perhousehold in the community No; country club members would tend to bemore affluent and thus not a representative sample of the community.
5. surveying all students whose ID numbers end in 4 about their grades and careercounseling needs Yes; ID numbers are probably assigned alphabetically orby some other method not connected to students’ grades or counselingneeds.
6. surveying parents at a day care facility about their preferences for brands of baby foodfor a marketing campaign Yes; choice of a daycare facility would probablynot influence baby food preferences.
7. asking people in a library about the number of magazines to which they subscribe inorder to describe the reading habits of a town No; library visitors tend to readmore than most citizens.
ExampleExample
ExercisesExercises
© Glencoe/McGraw-Hill 748 Glencoe Algebra 2
Margin of Error The margin of sampling error gives a limit on the differencebetween how a sample responds and how the total population would respond.
If the percent of people in a sample responding in a certain way is p and the size of the sample Margin of Error is n, then 95% of the time, the percent of the population responding in that same way will be
between p � ME and p � ME, where ME � 2�.
In a survey of 4500 randomly selected voters, 62% favoredcandidate A. What is the margin of error?
ME � 2� Formula for margin of sampling error
� 2� p � 62% or 0.62, n � 4500
� 0.01447 Use a calculator.
The margin of error is about 1%. This means that there is a 95% chance that the percent ofvoters favoring candidate A is between 62 � 1 or 61% and 62 � 1 or 63%.
The CD that 32% of teenagers surveyed plan to buy next is thelatest from the popular new group BFA. If the margin of error of the survey is 2%,how many teenagers were surveyed?
ME � 2� Formula for margin of sampling error
0.02 � 2� ME � 0.02, p � 0.32
0.01 � � Divide each side by 2.
0.0001 � Square each side.
n � Multiply by n and divide by 0.0001
n � 2176
2176 teenagers were surveyed.
Find the margin of sampling error to the nearest percent.
1. p � 45%, n � 350 2. p � 12%, n � 1500 3. p � 86%, n � 600about 5% about 2% about 3%
4. A study of 50,000 drivers in Indiana, Illinois, and Ohio showed that 68% preferred aspeed limit of 75 mph over 65 mph on highways and country roads. What was themargin of sampling error to the nearest tenth of a percent? about 0.4%
0.32(0.68)��0.0001
0.32(0.68)��n
0.32(0.68)��n
0.32 � (1 � 0.32)��n
p(1 � p)��n
0.62 � (1 � 0.62)��4500
p(1 � p)��n
p(1 � p)��
n
Study Guide and Intervention (continued)
Sampling and Error
NAME ______________________________________________ DATE ____________ PERIOD _____
12-912-9
Example 1Example 1
Example 2Example 2
ExercisesExercises
Skills PracticeSampling and Error
NAME ______________________________________________ DATE ____________ PERIOD _____
12-912-9
© Glencoe/McGraw-Hill 749 Glencoe Algebra 2
Less
on
12-
9
Determine whether each situation would produce a random sample. Write yes orno and explain your answer.
1. calling households at 3:30 P.M. on Tuesday to determine a political candidate’s supportNo; since most registered voters are likely to be at work at this time, thissample would not be representative of all registered voters.
2. polling customers as they exit a sporting goods store about their attitudes about exerciseNo; these customers are likely to value exercise more than those who donot shop at sporting goods stores, who are not represented in this survey.
3. recording the number of sit-ups performed by 15-year old girls in the high schools of alarge school district to determine the fitness of all high-school girls in the districtNo; 15-year old girls may not have the same abilities as 18-year oldseniors, for example.
4. selecting two of a city’s 20 apartment buildings for a survey to determine the desire ofapartment dwellers in the city to own a home No; the residents of the twobuildings selected might, for example, have nicer apartments or be in anicer area of town, and thus would not well represent the desires ofpeople in other buildings.
5. In a large school district, the superintendent of schools interviews two teachers atrandom from each school to determine whether teachers in the district think studentsare assigned too much or too little homework. Yes; since a cross section ofteachers from all levels was selected at random, the sample should wellrepresent the population of teachers in the district.
6. For seven consecutive days, one hour each in the morning, afternoon, and evening, everytenth customer who enters a mall is asked to choose her or his favorite store. Yes;because the sample is chosen over the course of a whole week, duringhours when different consumer groups shop, and because the selectionis systematic, the sample should well represent the general populationthat shops at the mall stores.
Find the margin of sampling error to the nearest percent.
7. p � 85%, n � 100 about 7% 8. p � 78%, n � 100 about 8%
9. p � 15%, n � 100 about 7% 10. p � 37%, n � 500 about 4%
11. p � 12%, n � 500 about 3% 12. p � 93%, n � 500 about 2%
13. p � 23%, n � 1000 about 3% 14. p � 56%, n � 1000 about 3%
15. HEALTH In a recent poll of cigarette smokers, 67% of those surveyed said they had triedto quit smoking within the last year. The margin of error was 3%. About how manypeople were surveyed? about 983
© Glencoe/McGraw-Hill 750 Glencoe Algebra 2
Determine whether each situation would produce a random sample. Write yes orno and explain your answer.
1. calling every twentieth registered voter to determine whether people own or rent theirhomes in your community No; registered voters may be more likely to behomeowners, causing the survey to underrepresent renters.
2. predicting local election results by polling people in every twentieth residence in all thedifferent neighborhoods of your community Yes; since all neighborhoods arerepresented proportionally, the views of the community should as awhole should be well represented.
3. to find out why not many students are using the library, a school’s librarian gives aquestionnaire to every tenth student entering the library No; she is polling onlythe students who are coming to the library, and will obtain no input fromthose who aren’t using the library.
4. testing overall performance of tires on interstate highways only No; for overallperformance, tires should be tested on many kinds of surfaces, andunder many types of conditions.
5. selecting every 50th hamburger from a fast-food restaurant chain and determining itsfat content to assess the fat content of hamburgers served in fast-food restaurant chainsthroughout the country No; the selected hamburgers are a random sampleof the hamburgers served in one chain, and may represent the fatcontent for that chain, but will not necessarily represent the fat contentof hamburgers served in other fast-food restaurant chains.
6. assigning all shift workers in a manufacturing plant a unique identification number, andthen placing the numbers in a hat and drawing 30 at random to determine the annualaverage salary of the workers Yes; because the numbers are randomlychosen from among all shift workers, all workers have the same chanceof being selected.
Find the margin of sampling error to the nearest percent.
7. p � 26%, n � 100 8. p � 55%, n � 100 9. p � 75%, n � 500about 9% about 10% about 4%
10. p � 14%, n � 500 11. p � 96%, n � 1000 12. p � 21%, n � 1000about 3% about 1% about 3%
13. p � 34%, n � 1000 14. p � 49%, n � 1500 15. p � 65%, n � 1500about 3% about 3% about 2%
16. COMPUTING According to a poll of 500 teenagers, 43% said that they use a personalcomputer at home. What is the margin of sampling error? about 4%
17. TRUST A survey of 605 people, ages 13–33, shows that 68% trust their parents more thantheir best friends to tell them the truth. What is the margin of sampling error? about 4%
18. PRODUCTIVITY A study by the University of Illinois in 1995 showed an increase inproductivity by 10% of the employees who wore headsets and listened to music of theirchoice while they were working. The margin of sampling error for the study was about7%. How many employees participated in the study? about 76
Practice (Average)
Sampling and Error
NAME ______________________________________________ DATE ____________ PERIOD _____
12-912-9
Reading to Learn MathematicsSampling and Error
NAME ______________________________________________ DATE ____________ PERIOD _____
12-912-9
© Glencoe/McGraw-Hill 751 Glencoe Algebra 2
Less
on
12-
9
Pre-Activity How are opinion polls used in political campaigns?
Read the introduction to Lesson 12-9 at the top of page 682 in your textbook.
Do you think the results of the survey about the presidential preferencesdemonstrates that Bush was actually ahead in Florida a month before theelection? If there is not enough information given to determine this, list atleast two questions you would ask about the survey that would help youdetermine the significance of the survey. Sample answer: There is notenough information to tell. 1. How many people were surveyed?2. How was the sample for the survey selected? 3. What is themargin of error for this survey?
Reading the Lesson
1. Determine whether each situation would produce a random sample. Write yes or no andexplain your answer.
a. asking all the customers at five restaurants on the same evening how many times amonth they eat dinner in restaurants to determine how often the average Americaneats dinner in a restaurants No; people surveyed at a restaurant might belikely to eat dinner in restaurants more often than other people.
b. putting the names of all seniors at your high school in a hat and then drawing 20 namesfor a survey to find out where seniors would like to hold their prom Yes; everysenior would have an equal chance of being chosen for the survey.
2. A survey determined that 58% of registered voters in the United States support increasedfederal spending for education. The margin of error for this survey is 4%. Explain in yourown words what this tells you about the actual percentage of registered voters who supportincreased spending for education. Sample answer: There is a 95% chance thatthe actual percentage of voters supporting increased federal spendingfor education is between 54% and 62%.
Helping You Remember
3. The formula for margin of sampling error may be tricky to remember. A good way to startis to think about the variables that must be included in the formula. What are thesevariables, and what do they represent? What is an easy way to remember which variablegoes in the denominator in the formula? Sample answer: p is the probability ofa certain response and n is the sample size. The larger the sample size,the smaller the margin of error, so n must go in the denominator sincedividing by a larger number gives a smaller number. The square root of asmaller number is a smaller number, and twice the square root of asmaller number is a smaller number.
© Glencoe/McGraw-Hill 752 Glencoe Algebra 2
Shapes of Distribution CurvesGraphs of frequency distributions can be described as either symmetric or skewed.
In a distribution skewed to the right, there are a larger number of highvalues. The long “tail” extends to the right.
In a distribution skewed to the left, there are a larger number of low values.The “tail” extends to the left.
For each of the following, state whether the distribution is symmetricor skewed. If it is skewed, tell whether it is skewed to the right or tothe left.
1. 2. 3.
symmetric skewed to the left skewed to the right
4. 5. 6.
symmetric symmetric skewed to the right
A vertical line above the median divides the area under a frequencycurve in half.
7. Where is the median in a symmetric 8. Where is the median in a skeweddistribution? In the middle of the distribution? To the left of the middle range; it is the same as the mean. if skewed to the right; to the right
of the middle if skewed to the left.
Symmetric Skewed to the Right Skewed to the Left
MedianModeMean Median
Mode Mean
Median
ModeMean
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
12-912-9
Write the letter for the correct answer in the blank at the right of each question.
1. Carl purchased four new shirts and three new pairs of pants. How many new outfits can he make with these items?A. 12 B. 7 C. 9 D. 81 1.
2. TRIATHALON During training, a triathlete works on biking, swimming,and running times. How many ways can a triathlete choose the order of these activities in a training session?A. 4 B. 9 C. 5 D. 6 2.
3. Evaluate P(7, 2).A. 49 B. 21 C. 42 D. 14 3.
4. Evaluate C(6, 2).A. 30 B. 15 C. 12 D. 36 4.
5. Find the odds of an event occurring, given that the probability of the event
is �131�.
A. 3:11 B. 8:3 C. 8:11 D. 3:8 5.
6. The table and relative-frequency histogram show the distribution of the number of tails when 2 coins are tossed. Find P(T � 2 tails).
A. �14� B. �
12�
C. 1 D. 0 6.
7. A blue die and a red die are tossed. What is the probability that a 6 will appear on both dice?
A. �118�
B. �316�
C. �12� D. �1
11�
7.
8. A jar contains 10 purple marbles and 2 red marbles. If two marbles are chosen at random with no replacement, what is the probability that 2 purple marbles are chosen?
A. �2356�
B. �56� C. �
1252�
D. �15� 8.
9. A bag contains 6 cherry, 8 strawberry, and 9 grape-flavored candies. What is the probability of selecting a cherry or a grape flavored candy?
A. �1253�
B. �1243�
C. �1273�
D. �55249�
9.
10. A die is rolled. What is the probability of rolling a 6 or a number greater than 4?
A. �23� B. �
12� C. �
16� D. �
13� 10.
11. A coin is tossed 5 times. Find P(5 tails).
A. �15� B. �1
10�
C. �116�
D. �312�
11.
Chapter 12 Test, Form 1
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 753 Glencoe Algebra 2
Ass
essm
ent
1212
T � Tails 0 1 2
Probability �14
� �12
� �14
�210
0
Pro
bab
ility
Tails
12
34
14
© Glencoe/McGraw-Hill 754 Glencoe Algebra 2
Chapter 12 Test, Form 1 (continued)
12. Which measure of central tendency best represents a data set with outliers?A. mode B. mean C. median D. variance 12.
For Questions 13–15, use the data set {10, 12, 12, 14, 22}.
13. Find the mean.A. 17.5 B. 14 C. 70 D. 13 13.
14. Find the variance. Round to the nearest tenth, if necessary.A. 17.6 B. 88 C. 4.2 D. 4 14.
15. Find the standard deviation. Round to the nearest tenth, if necessary.A. 17.6 B. 14.6 C. 4.2 D. 14 15.
16. Classify the data in the table.A. positively skewedB. negatively skewedC. normally distributedD. discrete distribution 16.
17. CAR SALES The mean stay of a car on a lot before being sold is 21 days, with a standard deviation of 3 days. The lengths of stay are normally distributed. What percent of the cars are sold after having been on the lot between 18 and 24 days?A. 95% B. 34% C. 68% D. 5% 17.
18. The probability that a certain team will win a baseball game is �13�. In a
5-game series, what is the probability that the team will win all five games?
A. �115�
B. �2143�
C. �13� D. �2
543�
18.
19. COMMUTERS Which group should be surveyed to determine how people commute to work in order to produce a random sample?A. students in your schoolB. people passing through a toll booth on a given dayC. people in your state whose last name begins with SD. people whose annual income is greater than $1,000,000 19.
20. Find the margin of sampling error when p � 45% and n � 100 if
ME � 2��p(1
n�� p)��.
A. 9% B. 10% C. 5% D. 1% 20.
Bonus If f represents the probability of rolling a 5 and nrepresents the probability of rolling any other number,which term of (f � n)4 � f 4 � 4f 3n � 6f 2n2 � 4fn3 � n4
represents the probability of rolling exactly three 5s in 4 rolls of a die? Find the probability. B:
NAME DATE PERIOD
1212
Amount Spent on LunchLess than $4.00 18%
$4.00–$7.99 47%
$8.00–$11.99 16%
$12.00–$15.99 11%
$16.00 or more 8%
Chapter 12 Test, Form 2A
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 755 Glencoe Algebra 2
Ass
essm
ent
Write the letter for the correct answer in the blank at the right of each question.
1. LICENSE PLATES A license plate has one letter (not I or O) followed by five digits. How many different plates are possible?A. 1200 B. 2,400,000 C. 725,760 D. 100,000 1.
2. How many 3-letter identification codes are possible if no letter is repeated?A. 17,576 B. 2600 C. 78 D. 15,600 2.
3. Evaluate P(10, 4).A. 5040 B. 151,200 C. 30,240 D. 210 3.
4. A group has 6 men and 5 women. How many ways can a committee of 3 men and 2 women be formed?A. 200 B. 150 C. 7200 D. 2400 4.
5. The odds that an event will occur are 7:2. What is the probability that the event will occur?
A. �194�
B. �79� C. �
29� D. �
27� 5.
6. Two marbles are chosen at random from a bag containing 3 blue and 2 red marbles. The relative-frequency histogram shows the distribution of the number of red marbles chosen. Find P(2 red).
A. �110�
B. �15�
C. �35� D. �1
30�
6.
7. A red die and a blue die are tossed. What is the probability that the red die shows a 5 and the blue die shows an even number?
A. �316�
B. �118�
C. �112�
D. �23� 7.
8. Tickets are numbered 1 to 50 and are placed in a box. Three tickets are drawn at random without replacement. What is the probability that the numbers are all greater than 35?
A. �120700� B. �5
1630�
C. �130�
D. �78140� 8.
9. From 4 yellow and 9 blue marbles, 3 are selected. What is the probability that all 3 are yellow or all 3 are blue?
A. �1443�
B. �143�
C. �14423�
D. �18443�
9.
10. A card is drawn from a deck of cards. What is the probability of drawing a club or a face card? (Hint: A face card is a jack, queen, or king.)
A. �2552�
B. �133�
C. �2161� D. �1
73�
10.
11. A coin is tossed 5 times. Find P(at least 3 tails).
A. �136�
B. �12� C. �1
56�
D. �35� 11.
1212
2100
Pro
bab
ility
Red
15
25
3512
310
110
© Glencoe/McGraw-Hill 756 Glencoe Algebra 2
Chapter 12 Test, Form 2A (continued)
12. How many different arrangements of the letters of the word radar are possible?A. 120 B. 60 C. 30 D. 480 12.
TEMPERATURES For Questions 13–15, use the data in the table. Round to the nearest tenth, if necessary.
Source: www.weather.com
13. Which measure of central tendency is not a good representation of the data?A. mean B. mode C. median D. middle 13.
14. Find the variance of the temperatures.A. 28.4 B. 5.3 C. 59.3 D. 340.7 14.
15. Find the standard deviation of the temperatures.A. 52�F B. 5.3�F C. 5.6�F D. 28.4�F 15.
16. Classify the data in the table.A. positively skewedB. negatively skewedC. normally distributedD. discrete distribution 16.
17. POTTERY The diameters of pottery bowls are normally distributed. The mean of the diameters is 22 cm and the standard deviation is 2 cm. What percent of the bowls have diameters between 18 and 26 cm?A. 13.5% B. 34% C. 68% D. 95% 17.
18. In a local car lot, �16� of the cars have standard transmissions. Find the
probability that 3 of 4 randomly-selected cars have standard transmissions.
A. �132254�
B. �59� C. �3
524�
D. �12596� 18.
19. A school librarian wants to determine the reading interests of students. A survey of which group would produce a random sample?A. every third student leaving the library on a given dayB. students on the football teamC. every fifth person entering the school in the morningD. seniors planning to attend college 19.
20. HOMEWORK In a survey of 320 students, 32% spent at least 1 hour per night on homework. Find the margin of sampling error.A. 5% B. 21% C. 3% D. 10% 20.
Bonus Write a data set having 7 values that has a median of 24 and a mean of 20. B:
NAME DATE PERIOD
1212
Record Low Temperatures in Honolulu, HI (�F)Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
52 53 55 56 60 65 66 67 66 61 57 54
Age of Population of Iowa in 2000Age Number of People
0–24 978,875
25–44 795,499
45–64 644,861
65–84 357,074
Over 84 45,848
Chapter 12 Test, Form 2B
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 757 Glencoe Algebra 2
Ass
essm
ent
Write the letter for the correct answer in the blank at the right of each question. 1. An ice cream store has 31 flavors of ice cream and 10 toppings. A regular
sundae has one flavor of ice cream, one topping, and comes with or without whipped cream. How many different ice cream sundaes can be ordered?A. 310 B. 372 C. 620 D. 82 1.
2. How many 5-digit codes are possible if 0 cannot be used and no digit can be repeated?A. 15,120 B. 45 C. 30,240 D. 59,049 2.
3. A clown has 7 balloons, each a different color. There are 5 children.How many ways can the clown give each child a balloon?A. 21 B. 5040 C. 42 D. 2520 3.
4. Evaluate C(13, 9).A. 17,160 B. 715 C. 259,459,200 D. 117 4.
5. The probability that an event will occur is �1151�. What are the odds that the
event will occur?A. 15:11 B. 11:15 C. 4:11 D. 11:4 5.
6. Two marbles are chosen at random from a bag containing 3 blue and 2 red marbles. The relative-frequency histogram shows the distribution of the number of red marbles chosen. Find P(0 red).
A. 0 B. �185�
C. �115�
D. �25� 6.
7. A red die and a blue die are tossed. What is the probability that the red die shows a 3 and the blue die shows a number greater than 3?
A. �110�
B. �15� C. �1
30�
D. �35� 7.
8. Tickets are numbered 1 to 50 and placed in a box. Three tickets are drawn at random without replacement. What is the probability that their numbers are all greater than 25?
A. �18� B. �1
2936�
C. �66295�
D. �12� 8.
9. From 4 yellow and 8 blue marbles, 3 are selected. What is the probability that all three are yellow or all three are blue?
A. �131�
B. �515�
C. �1545�
D. �2320�
9.
10. A card is drawn from a standard deck of cards. What is P(heart or a 6)?
A. �296�
B. �1572�
C. �14� D. �1
43�
10.
11. A coin is tossed 5 times. Find P(at most 4 tails).
A. �136�
B. �1136�
C. �312�
D. �3312�
11.
1212
2100
Pro
bab
ility
Red
15
25
3512
310
110
© Glencoe/McGraw-Hill 758 Glencoe Algebra 2
Chapter 12 Test, Form 2B (continued)
12. How many different arrangements of the letters of the word doodle are possible?A. 180 B. 720 C. 15 D. 90 12.
TEMPERATURES For Questions 13–15, use the data in the table. Round to the nearest tenth, if necessary.
Source: www.weather.com
13. Which measure of central tendency is not a good representation of the data?A. middle B. median C. mode D. mean 13.
14. Find the variance of the temperatures.A. 4366.2 B. 64.6 C. 2342.9 D. 195.2 14.
15. Find the standard deviation of the temperatures.A. 14.6�F B. 14.0�F C. 63.0�F D. 64.6�F 15.
16. Classify the data in the table.A. positively skewedB. negatively skewedC. normally distributedD. discrete distribution 16.
17. For 2000 patients, blood-clotting time was normally distributed with a mean of 8 seconds and a standard deviation of 3 seconds. What percent had blood-clotting times between 5 and 11 seconds?A. 68% B. 34% C. 49.5% D. 47.5% 17.
18. During a sale, �16� of the CD prices are reduced. Find the probability that 2
of 4 randomly-selected CDs have reduced prices.
A. �356�
B. �122596� C. �2
2156�
D. �2516�
18.
19. A music teacher wants to determine the music preferences of students.A survey of which group would produce a random sample?A. students in the school bandB. students attending the annual jazz concertC. students in every odd-numbered homeroomD. every other player on the baseball roster 19.
20. ELECTIONS In an election poll, 56% of 400 voters chose a certain candidate. Find the margin of sampling error.A. 5% B. 2% C. 4% D. 7% 20.
Bonus Write a data set having 7 data values that has a median of 20 and a mean of 24. B:
NAME DATE PERIOD
1212
Record High Temperatures in Anchorage, Alaska (�F)Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
50 48 51 65 77 85 82 82 73 61 53 48
Source: Census 2000
Age of Population of Rhode Island in 2000
Age Number of People
0–14 206,423
15–34 265,778
35–54 308,946
55–74 159,092
over 74 69,264
Chapter 12 Test, Form 2C
© Glencoe/McGraw-Hill 759 Glencoe Algebra 2
1. BELTS A clothing store sells belts in 3 colors, 4 designs, and 1.6 sizes. How many different belts are available?
2. Five children stand in a line to play a game. How many 2.different ways can the children be arranged?
3. CROSS-COUNTRY Twelve runners are in a cross-country 3.race. How many different ways can they finish first, second,and third?
4. Five cheerleaders will be chosen from a group of 15 students. 4.How many different cheerleading squads can be formed?
5. The odds of an event occurring are 4 to 7. What is the 5.probability that the event will occur?
6. Two socks are chosen at random from 6.a drawer containing 6 black and 3 blue socks. The table and relative-frequency histogram show the distribution of the number of black socks chosen. Find P(B � 2).
7. A die is rolled three times. What is P(no 5s)? 7.
8. Two cards are drawn from a standard deck of 52 cards 8.without replacement. Find the probability that the first card is an ace and the second is a 2.
9. From a group of 6 men and 8 women, a committee of 3 is 9.selected. Find the probability that all 3 are men or all 3 are women.
10. Each of the numbers 1 to 25 is written on a card and placed 10.in a bag. If one card is drawn at random, what is the probability that it is a multiple of 4 or a multiple of 5?
11. Seven coins are tossed. Find P(at least 6 tails). 11.
12. If the probability of rain in a certain city is �18� on any given 12.
day, find the probability that rain will fall on exactly one day of a three-day visit to the city.
13. How many different arrangements of the letters in the word 13.ILLINOIS are possible?
NAME DATE PERIOD
SCORE 1212
Ass
essm
ent
B � Black 0 1 2
Probability �112� �
12
� �152� 210
0
Pro
bab
ility
Black
16
13
125
12
14
112
© Glencoe/McGraw-Hill 760 Glencoe Algebra 2
Chapter 12 Test, Form 2C (continued)
TEMPERATURES For Questions 14–16, use the data in the table.Round to the nearest tenth, if necessary.
Source: www.weather.com
14. If you were a member of the Chamber of Commerce, which 14.measure of central tendency would you use to convince someone that Memphis has a comfortable climate? Explain.
15. Find the variance of the temperatures. 15.
16. Find the standard deviation of the temperatures. 16.
17. EDUCATION Determine whether the data in the table is 17.positively skewed, negatively skewed, or normally distributed.
Source: www.census.gov
18. COLLEGE ENTRANCE EXAM The scores on a standardized 18.college entrance examination are found to be normally distributed. The mean is 85 and the standard deviation is 11.What percent scored between 85 and 107?
19. Determine whether the situation would produce a random 19.sample and explain your answer: surveying your class to determine the most-admired person in the United States by people your age.
20. In a sample of 120 small business owners, 64% said they 20.preferred a certain company for office supplies. Find the margin of sampling error.
Bonus Student test grades were normally distributed, and B:grades between 62 and 86 were within three standard deviations of the mean. Find the mean and standard deviation of the set of grades.
NAME DATE PERIOD
1212
Educational Attainment in Georgia for persons over 25 years of age, as of 2000
Less than 9th grade 484,000
9th to 12th grade, no diploma 686,000
High school graduate 1,193,000
Some college or associate degree 884,000
Bachelor’s degree 520,000
Graduate or professional degree 258,000
Record High Temperatures in Memphis, TN (�F)Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
78 81 85 94 99 104 108 105 103 95 85 81
Chapter 12 Test, Form 2D
© Glencoe/McGraw-Hill 761 Glencoe Algebra 2
1. A store sells T-shirts in 7 colors, 5 designs, and 3 sizes. How 1.many different T-shirts are available?
2. Marva needs to mow the lawn, pay her bills, walk the dog, 2.and return a phone call. How many ways can she choose to order her tasks?
3. How many different arrangements of three coins can be 3.made if you have a penny, a nickel, a dime, a quarter, and a silver dollar?
4. How many different 5-player basketball teams can be 4.formed from a group of 12 people?
5. If the probability that an event will occur is �152�
, what are 5.
the odds that it will occur?
6. Two socks are chosen at random from 6.a drawer containing 4 black and 3 blue socks. The table and relative-frequency histogram show the distribution of the number of blue socks chosen. Find P(B � 1).
7. A die is rolled three times. What is P(three 5s)? 7.
8. Two cards are drawn from a standard deck of 52 cards 8.without replacement. Find the probability that both cards are aces.
9. From a group of 7 men and 5 women, a 4-person committee 9.is chosen. What is the probability that all 4 are men or all 4 are women?
10. Each of the numbers 1 to 20 is written on a card and placed 10.in a bag. If one card is drawn at random, what is the probability that it is a multiple of 3 or a multiple of 5?
11. Eight coins are tossed. Find P(at least 7 heads). 11.
12. If the probability of rain in a certain city is �25� on any given 12.
day, find the probability that rain will fall on exactly one day of a three-day visit to the city.
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Ass
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B � Blue 0 1 2
Probability �27
� �47
� �17
�
2100
Pro
bab
ility
Blue
17
27
37
47
© Glencoe/McGraw-Hill 762 Glencoe Algebra 2
Chapter 12 Test, Form 2D (continued)
13. How many different arrangements of the letters in the word INDIANA are possible? 13.
14. The sales prices of several cars on a used car lot are 14.$18,900; $20,500; $29,900; $19,800; and $21,750. Which measure of central tendency best represents the data? Explain.
For Questions 15 and 16, use the data in the table that shows average precipitation in Grand Junction,Colorado. Round to the nearest hundredth, if necessary.
Source: www.weather.com
15. Find the variance of the data. 15.
16. Find the standard deviation of the data. 16.
17. Determine whether the data 17.in the table is positively skewed, negatively skewed,or normally distributed.
18. COLLEGE ENTRANCE EXAM The scores on a 18.standardized college entrance examination are found to be normally distributed. The mean is 78 and the standard deviation is 13. What percent scored between 52 and 78?
19. Determine whether the situation would produce a random 19.sample and explain your answer: surveying persons with library cards to determine if a city should raise taxes to pay for a new library.
20. In a survey of 60 customers in a supermarket, 40% expect to 20.use the express line. What is the margin of sampling error?
Bonus Student test grades were normally distributed, and B:grades between 68 and 86 were within three standard deviations of the mean. Find the mean and standard deviation of the set of grades.
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Age of Population of Florida in 2000
Age Number of People
0–24 4,870,160
25–44 4,442,638
45–64 3,581,676
65–84 2,449,573
Over 84 269,388
Average Precipitation in Grand Junction, CO (in.)Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
0.6 0.5 0.9 0.8 0.9 0.5 0.7 0.8 0.8 1.0 0.7 0.6
Source: Census 2000
Chapter 12 Test, Form 3
© Glencoe/McGraw-Hill 763 Glencoe Algebra 2
1. Each day, Jonathan chooses one of six routes to work. How 1.many different ways can Jonathan get to work over a five-day period?
2. How many different ways can 9 entertainers appear on an 2.awards show if the guest of honor must appear first or last?
3. How many ways can you select 4 pizza toppings from a total 3.of 8 toppings? Is this a permutation or a combination? Explain.
4. Evaluate C(13, 5) � C(9, 4). 4.
5. A coin purse contains 4 pennies, 5 nickels, and 8 dimes. 5.Three coins are selected at random. Find the probability of selecting one coin of each type.
6. Three students are selected at 6.random from a group of 4 males and 6 females. The table and relative-frequency histogram show the distribution of the number of males chosen. Find P(two females).
7. A die is rolled four times. Find P(four of the same number). 7.
8. Four cards are drawn from a standard deck of 52 cards 8.without replacement. Find the probability that the first card is a heart, the second is a club, and the third and fourth are diamonds.
9. From a group of 8 men and 10 women, a committee of 5 is 9.to be selected at random. Find P(at least 3 men).
10. Two cards are drawn from a standard deck of cards. Find 10.P(both black or both 9s).
11. How many ways can 4 basketball shoes, 2 tennis shoes, and 11.5 running shoes be arranged on a shelf if the shoes are grouped according to type?
NAME DATE PERIOD
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Ass
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M � Male 0 1 2
Probability �16
� �12
� �130� �
310�
3
32100
Pro
bab
ility
Males
110
730
1130
1330
12
310
16
130
© Glencoe/McGraw-Hill 764 Glencoe Algebra 2
Chapter 12 Test, Form 3 (continued)
TAXES For Questions 12–15, use the data in the table that shows the per capita taxes, in dollars, in the 10 states listed. Round to the nearest cent, if necessary.
Source: World Almanac
12. Which measure of central tendency might a realtor in 12.Maryland use to convince a client that the per capita taxes were reasonable? Explain.
13. Find the variance of the taxes. 13.
14. Find the standard deviation of the taxes. 14.
15. Determine whether the data in the table is positively 15.skewed, negatively skewed, or normally distributed.
16. IQ TESTS Scores on an IQ test are normally distributed. 16.The mean is 100 and the standard deviation is 15. If 6000 people took the test, how many of them scored between 85 and 130?
17. Find P(at least four 4s) if a die is rolled 6 times. 17.
18. In a certain city in June, the probability that the 18.temperature will rise above 80�F is 0.7. For the first 8 days,what is P(temperature will rise above 80�F exactly 3 times)?Round to the nearest hundredth.
19. Determine whether the situation would produce a random 19.sample and explain your answer: surveying town residents whose license number ends in 5 to determine whether to increase taxes to pay for road repair.
20. PETS In a survey of pet owners, 68% preferred dogs to any 20.other kind of pet. The margin of sampling error was 5%.How many people were surveyed?
Bonus 20% of the students in a high school were surveyed to B:determine their favorite pizza topping. If 43% of those surveyed responded “pepperoni,” and the margin of sampling error was 6.2%, how many students attend the high school?
NAME DATE PERIOD
1212
State Taxes State TaxesArizona 1489 Iowa 1678
California 2073 Maine 1905
Colorado 1483 Maryland 1790
Delaware 2665 Michigan 2161
Illinois 1641 Missouri 1512
Chapter 12 Open-Ended Assessment
© Glencoe/McGraw-Hill 765 Glencoe Algebra 2
Demonstrate your knowledge by giving a clear, concise solutionto each problem. Be sure to include all relevant drawings andjustify your answers. You may show your solutions in more thanone way or investigate beyond the requirements of the problem.
1. Kathy, Alma, and Steven are working on a group quiz. Onequestion is as follows.Two dice are rolled. Find the probability that the first die is a 5 ora 6, and the second die is an even number.All three students agree to let A represent rolling a 5 or a 6, and B represent rolling an even number. But Kathy argues that the
solution is P(A) � P(B) � �26� � �
36� � �
56�, Alma feels certain that the
solution should be P(A) � P(B) � �26� � �
36� � �3
66�
� �16�, and Steven is
convinced that the correct solution is P(A) � P(B) � P(A and B) �
�26� � �
36� � �
16� � �
46� � �
23�.
a. Which student, if any, is correct? Explain your reasoning.b. For one of the incorrect solutions above, write a probability
problem for which that solution would be correct.2. a. One day, your math teacher, Mr. Butler, looks at your exam
scores and informs you that your score distribution isnegatively skewed. How do you feel about this news? Explainyour reasoning.
b. The next day, Mr. Butler announces that the class scores on thelast exam were normally distributed, that scores between 56and 98 fell within three standard deviations of the mean, andthat students whose scores fell within one standard deviationof the mean would earn a grade of C on the exam. Explain howto estimate the mean score, the standard deviation of the classscores, and the range of grades for which a student would earna grade of C. Determine the indicated values.
3. Greg and Jacqui are planning a dinner party for 6 guests. Afterdinner, they plan to separate into two teams to play charades.a. Explain how you could determine the number of different
possible arrangements of guests and hosts into two teams.Include in your explanation whether the formula
P(n, r) � �(n �n!
r)!� or the formula C(n, r) � �(n �n!
r)!r!� would be
helpful in determining the number of arrangements. Explainyour reasoning and determine the number of arrangementsthat are possible.
b. Would the number of possible arrangements change if Gregand Jacqui decided that they should be on different teams? If so, how many arrangements would be possible under thoseconditions? Explain your reasoning.
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© Glencoe/McGraw-Hill 766 Glencoe Algebra 2
Chapter 12 Vocabulary Test/Review
Write whether each sentence is true or false. If false, replace the underlined word or words to make a true sentence.
1. A selection of objects in which order is not important is 1.called a permutation.
2. The graph of a normal distribution is a bell curve. 2.
3. Range, variance, and odds are measures of the spread of a 3.set of data.
4. Probability distributions with a finite number of possible 4.values are called continuous probability distributions.
5. Tossing a coin ten times is an example of a 5.linear permutation.
6. A relative-frequency distribution is a graph of a 6.probability distribution.
7. Two or more choices for which the result of one choice does 7.not affect the result of another are called independent events.
8. Events that consist of two or more simple events are called 8.dependent events.
9. The mean, the median, and the mode are 9.measures of variation.
10. A curve or histogram that is not symmetric represents a(n) 10.unbiased sample.
In your own words—Define each term.
11. mutually exclusive events
12. random sample
area diagrambinomial experimentcombinationcompound eventcontinuous probability distribution
dependent eventsdiscrete probability distributions
event
failureFundamental Counting Principle
inclusive eventsindependent eventslinear permutationmargin of sampling errormeasure of central tendency
measure of variation
mutually exclusive eventsnormal distributionoddsoutcomepermutationprobabilityprobability distributionrandomrandom variable
relative-frequency histogram
sample spacesimple eventskewed distributionstandard deviationsuccessunbiased samplevariance
NAME DATE PERIOD
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Chapter 12 Quiz (Lessons 12–1 through 12–3)
1212
© Glencoe/McGraw-Hill 767 Glencoe Algebra 2
1. Standardized Test Practice Lisa selects a car from 4 models. Each model comes in 5 colors. How many different ways can she select a car?A. 24 B. 16 C. 9 D. 20 1.
2. How many four-digit codes are possible if no digit may be 2.used more than once?
3. A group of 3 women and 1 man is chosen from 7 women and 3.5 men. Does this involve a permutation or a combination? Find the number of different groups that can be formed.
4. Cards are numbered 1 through 20. Find the probability that 4.a card drawn at random will contain a number greater than 11. Then find the odds that a number greater than 11 is drawn.
5. Two marbles are 5.chosen at random from a bag containing 4 red and 3 blue marbles. The table and relative-frequency histogram show the distribution of the number of red marbles chosen. Find P(R � 2).
NAME DATE PERIOD
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Chapter 12 Quiz (Lessons 12–4 and 12–5)
1. A pair of dice is thrown. What is the probability that both 1.dice show a number less than 5?
For Questions 2 and 3, consider a bag that contains 8 red marbles, 5 white marbles, and 2 blue marbles.
2. If 3 marbles are selected in succession with replacement, 2.what is the probability that the marbles are white, blue,and red in that order?
3. If 3 marbles are selected in succession without replacement, 3.what is the probability that the marbles are white, blue, and red in that order?
4. Janet has 3 dimes and 6 nickels in her pocket. She selects 4.3 coins without replacement. What is the probability that she selects all dimes or all nickels?
5. A card is drawn from a standard deck of 52 playing cards. 5.What is the probability that a heart or face card is drawn? (Hint: A face card is a jack, queen, or king.)
NAME DATE PERIOD
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Ass
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R � Red 0 1 2
Probability �17
� �47
� �27
�
2100
Pro
bab
ility
Red
17
27
37
47
© Glencoe/McGraw-Hill 768 Glencoe Algebra 2
1. Find the variance of the data set {13, 16, 17, 18, 16, 12, 14, 1.12}. Round to the nearest hundredth, if necessary.
2. Find the standard deviation for the data in Question 1. 2.Round to the nearest hundredth, if necessary.
3. Determine if the 3.data in the table appear to be positively or negatively skewed or normally distributed.
The times a group of high school students wake up on weekday mornings was found to be normally distributed.The mean wake-up time was 6:45 A.M. and the times had a standard deviation of 15 minutes.
4. What percent of the students would you expect to wake up 4.between 6:30 A.M. and 7:00 A.M.?
5. If 400 students were surveyed, how many would you expect 5.to wake up between 6:00 A.M. and 7:30 A.M.?
Chapter 12 Quiz (Lessons 12–8 and 12–9)
For Questions 1 and 2, find each probability if a die is rolled 3 times.
1. P(exactly two 4s) 2. P(at most two 4s)
3. A batter’s probability of getting a hit is �13�. In his next 3.
5 times at bat, what is the probability that he will get at least 4 hits?
4. Determine whether the situation would produce a random 4.sample and explain your answer: surveying students on the basketball team to determine the favorite sport of students in your school.
5. In a survey of 50 people, 80% read a newspaper at least 5.once per week. Find the margin of sampling error.
NAME DATE PERIOD
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Chapter 12 Quiz (Lessons 12–6 and 12–7)
1212
NAME DATE PERIOD
SCORE
1212
Family Income and Benefits in 2000
Income and Benefits Number of Families (in millions)
less than $50,000 35.8
$50,000–$99,999 24.3
$100,000–$149,999 6.9
$150,000–$199,999 2.0
$200,000 or more 1.9
1.
2.
Chapter 12 Mid-Chapter Test (Lessons 12–1 through 12–4)
© Glencoe/McGraw-Hill 769 Glencoe Algebra 2
Write the letter for the correct answer in the blank at the right of each question.
1. A company manufactures bicycles in 8 different styles. Each style comes in 7 different colors. How many different bicycles does the company make?A. 64 B. 49 C. 56 D. 15 1.
2. How many ways can 6 children form a line to use the drinking fountain?A. 120 B. 720 C. 36 D. 30 2.
3. Find P(9, 4).A. 126 B. 15,120 C. 36 D. 3024 3.
4. Find C(10, 8).A. 1,814,400 B. 80 C. 90 D. 45 4.
5. The probability that an event will occur is �27�. What are the odds that the
event will occur?A. 2:5 B. 5:2 C. 2:7 D. 2:9 5.
6. A die is rolled twice. Find P(4, then 5).
A. �310�
B. �13� C. �3
16�
D. �59� 6.
7. A jar contains 7 red, 8 blue, and 4 green marbles. What is 7.the probability of choosing 3 blue marbles in a row, if no replacement occurs?
8. A stained glass window has 25 blue pieces and 20 red pieces. 8.If 2 pieces are selected at random, what is P(2 red or 2 blue)?
9. SOCCER On the all-state soccer team, 5 of the 8 players 9.from the North Region are seniors, and 8 of the 12 players from the South Region are seniors. What is the probability that a randomly-selected student is a senior or is a student from the North Region?
10. How many different arrangements of three folders can be 10.made if you have one green, one red, one blue, and one black folder?
11. A bag contains 6 red dice and 10 blue dice. Two dice are 11.selected at random. Find the probability of selecting one red die and one blue die.
12. How many different groups of 3 students can be formed if 12.there are 20 students in the class?
Part II
Part I
NAME DATE PERIOD
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© Glencoe/McGraw-Hill 770 Glencoe Algebra 2
Chapter 12 Cumulative Review (Chapters 1–12)
1. The vertices of RST are R(�1, �3), S(2, 4), and T(�4, 3).The triangle is reflected over the line y � x. Find the coordinates of R�S�T�. (Lesson 4-4) 1.
2. Simplify (x2 � 3) � (4x2 � 5x � 9). (Lesson 5-2) 2.
3. Determine whether f(x) � 5x � 8 and g(x) � x � �85� are 3.
inverse functions. (Lesson 7-8)
For Questions 4 and 5, graph the function or equation.
4. (x � 5)2 � y2 � 9 (Lesson 8-3)
5. f(x) � ��(x �2
1)2� (Lesson 9-3)
6. Solve �ww� 3� � w � �w �
33�. Check your solution(s). (Lesson 9-6)
7. Write the equation log1000 �110�
� ��13� in exponential form.
(Lesson 10-2)
8. A savings account deposit of $500 is to earn 5.7% interest.After how many years will the investment be worth $750? Use y � a(1 � r)t and round to the nearest tenth. (Lesson 10-6)
9. Find the three arithmetic means between 5 and �7. (Lesson 11-1) 9.
10. Find four geometric means between 27 and �19�. (Lesson 11-3) 10.
11. Write 0.6�2�7� as a fraction. (Lesson 11-5) 11.
12. How many different ways can the letters of the word 12.PERMUTATION be arranged? (Lesson 12-2)
13. Three cards are drawn from a standard deck of cards 13.without replacement. Find the probability of drawing a king, a queen, and another king in that order. (Lesson 12-4)
14. The scores on an algebra test are found to be normally 14.distributed. The mean is 72 and the standard deviation is 8.What percent scored between 72 and 88? (Lesson 12-7)
NAME DATE PERIOD
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4.
5.
6.
7.
8.
xO
f (x )
y
xO
Standardized Test Practice (Chapters 1–12)
© Glencoe/McGraw-Hill 771 Glencoe Algebra 2
1. What is the seventh term in the sequence ��12�, �
14�, ��
18�, �1
16�
, …?
A. �614�
B. ��614�
C. �1128�
D. ��1128�
1.
2. In the correctly completed addition problem shown,� and � are nonzero digits. What number does �represent?E. 5 F. 7G. 4 H. 2 2.
3. The volume of a rectangular box is 405. The length, width,and height of the box are in the ratio 5 : 3 : 1. What is the total surface area of the box?A. 414 B. 27 C. 54 D. 324 3.
4. In the figure shown, what is the value of r?E. 10 F. 14G. 70 H. 7 4.
5. David is twice as old as his sister, Jennifer. Three years ago,David was three times as old as Jennifer. How old is David now?A. 12 B. 9 C. 6 D. 3 5.
6. If a � 0 and b 0, which of the following statements must be true?I. ab � 0 II. b � a 0 III. ac � bc
E. I, II, and III F. I onlyG. I and II only H. II and III only 6.
7. If (x � y)2 � 200 and x2 � y2 � 50, what is the value of xy?A. �75 B. 75 C. 150 D. �150 7.
8. What is 25% of 20% of �34�?
E. 0.375 F. 3.75 G. 0.00375 H. 0.0375 8.
9. What is the sum of all composite numbers between 1 and 15?A. 120 B. 59 C. 78 D. 63 9.
10. If (x � y)2 � 8 and (x � y)2 � 4, what is xy?E. 0 F. 1 G. 2 H. 3 10. HGFE
DCBA
HGFE
DCBA
HGFE
DCBA
HGFE
DCBA
HGFE
DCBA
NAME DATE PERIOD
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10r � 4t �
7t �
5r �
� 5* �
8 1� 1 �
1 6 0
Part 1: Multiple Choice
Instructions: Fill in the appropriate oval for the best answer.
© Glencoe/McGraw-Hill 772 Glencoe Algebra 2
Standardized Test Practice (continued)
11. Alejandra has been saving to purchase a VCR. 11. 12.The model she wants is priced at $180, on which she will be required to pay 5% sales tax. She has already saved $53. If Alejandra earns $8.50 per hour after all payroll deductions have been made, for how many hours will she need to work in order to have enough money to purchase the VCR?
12. If 43x�2 � 256, what is the value of 32x�1?
13. In the figure at the right, 13. 14.quadrilaterals ABCDand RSTU are similar.What is the value of n?
14. If the average of a and bis 87, the average of aand c is 73, and the average of b and c is 50,what is the average of a, b, and c?
Column A Column B15. d � 4 � 0 15.
16. y � �1, z 5 16.
17. h 0 17.
4h3 � 1�4h4
h� h�
DCBA
��zy
� � 1�z �
zy
�
DCBA
d33d
DCBA
Part 3: Quantitative Comparison
Instructions: Compare the quantities in columns A and B. Shade in if the quantity in column A is greater; if the quantity in column B is greater; if the quantities are equal; or if the relationship cannot be determined from the information given.
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.
99 9 987654321
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NAME DATE PERIOD
Part 2: Grid In
Instructions: Enter your answer by writing each digit of the answer in a column boxand then shading in the appropriate oval that corresponds to that entry.
D C
A
B
14 U
RS
T4
9
n
A
D
C
B
Unit 4 Test (Chapters 11–12)
© Glencoe/McGraw-Hill 773 Glencoe Algebra 2
1. Find the next four terms of the arithmetic sequence 1.4, 10, 16, … .
2. Find the three arithmetic means between 21 and 13. 2.
3. Find Sn for the arithmetic series in which a1 � �11, an � 13, 3.and n � 7.
4. Find the next two terms of the geometric sequence 4.6250, 5000, 4000, … .
5. Find four geometric means between 4096 and 972. 5.
6. Find the sum of a geometric series for which a1 � 1, r � 2, 6.and n � 6.
7. Find a1 in a geometric series for which Sn � 189, r � �12
�, and 7.an � 3.
8. Find the sum of the infinite geometric series 8.36 � 24 � 16 � …, if it exists.
9. Write 0.7�3�5� as a fraction. 9.
10. Find the first five terms of the sequence for which a1 � 5 10.and an�1 � 3an � 1.
11. Find the first three iterates x1, x2, x3 of f(x) � 2x � 5 for 11.an initial value of x0 � 3.
12. Use the Binomial Theorem to find the fifth term in the 12.expansion of (2x � 3y)5.
13. Prove that the statement �15� � �5
12� � �5
13� � … � �5
1n� � �
14��1 � �5
1n�� 13.
is true for all positive integers n. Write your proof on a separate piece of paper.
14. Find a counterexample to the statement 4n � 1 is divisible 14.by 5.
15. A scout troop will prepare trail mix for their next hike. 15.They have decided to mix one type of nut, one type of dried fruit, and one type of granola. The local store carries 8 types of nuts, 6 types of dried fruit, and 5 types of granola. How many different trail mixes are possible?
16. Students are given a list of ten vocabulary words to learn. In 16.how many ways could four of the words be listed on a test?
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© Glencoe/McGraw-Hill 774 Glencoe Algebra 2
Unit 4 Test (continued)(Chapters 11–12)
17. Evaluate C(12, 10). 17.
18. If the probability that an event will occur is �183�, what are 18.
the odds that it will occur?
19. A red die and a blue die are tossed. What is the probability 19.that the red die shows an odd number and the blue die shows a 1 or 2?
20. From a group of 6 men and 4 women, a committee of 3 is to 20.be selected at random. Find P(at least 2 women).
21. Two cards are drawn from a standard deck of cards. Find the 21.probability that a king or a red card is drawn.
For Questions 22 and 23, use the data in the table that shows the number of public secondary schools in eight eastern states in the fall of 1998.
22. Find the mean, median, 22.mode, and standard deviation of the data.Round to the nearest hundredth, if necessary.
23. Determine whether the 23.data in the table appear to be positively skewed,negatively skewed, or normally distributed.
24. The time a group of high school students arrive home from 24.school each day was found to be normally distributed. The mean time was 3:15 P.M. and the times had a standard deviation of 15 minutes. What is the probability that a student chosen at random arrives home from school before 2:30 P.M.?
25. During a clothing sale, �14� of the store merchandise is reduced 25.
in price. Find the probability that 3 of 5 randomly-selected shirts have reduced prices.
26. Determine whether the situation would produce a random 26.sample and explain your answer: surveying people at a concert to determine their favorite local radio station.
NAME DATE PERIOD
StateNumber of Public
Secondary SchoolsFlorida 456
Georgia 306
Maine 160
Massachusetts 363
North Carolina 376
New York 935
Rhode Island 54
Virginia 349
Source: World Almanac
Standardized Test PracticeStudent Record Sheet (Use with pages 694–695 of the Student Edition.)
© Glencoe/McGraw-Hill A1 Glencoe Algebra 2
NAME DATE PERIOD
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An
swer
s
Select the best answer from the choices given and fill in the corresponding oval.
1 4 7 9
2 5 8 10
3 6
Solve the problem and write your answer in the blank.
Also enter your answer by writing each number or symbol in a box. Then fill inthe corresponding oval for that number or symbol.
11 13 15
12 14
Select the best answer from the choices given and fill in the corresponding oval.
16 18 20
17 19 21 DCBADCBADCBA
DCBADCBADCBA
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.
99 9 987654321
87654321
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87654321
DCBADCBA
DCBADCBADCBADCBA
DCBADCBADCBADCBA
Part 2 Short Response/Grid InPart 2 Short Response/Grid In
Part 1 Multiple ChoicePart 1 Multiple Choice
Part 3 Quantitative ComparisonPart 3 Quantitative Comparison
© Glencoe/McGraw-Hill A2 Glencoe Algebra 2
Answers (Lesson 12-1)
Stu
dy G
uid
e a
nd I
nte
rven
tion
Th
e C
ou
nti
ng
Pri
nci
ple
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-1
12-1
©G
lenc
oe/M
cGra
w-H
ill69
9G
lenc
oe A
lgeb
ra 2
Lesson 12-1
Ind
epen
den
t Ev
ents
If t
he
outc
ome
of o
ne
even
t do
es n
ot a
ffec
t th
e ou
tcom
e of
anot
her
eve
nt
and
vice
ver
sa,t
he
even
ts a
re c
alle
d in
dep
end
ent
even
ts.
Fu
nd
amen
tal
If ev
ent
Mca
n oc
cur
in m
way
s an
d is
fol
low
ed b
y ev
ent
Nth
at c
an o
ccur
in n
way
s,
Co
un
tin
g P
rin
cip
leth
en t
he e
vent
Mfo
llow
ed b
y th
e ev
ent
Nca
n oc
cur
in m
�n
way
s.
FOO
DF
or t
he
Bre
akfa
st S
pec
ial
at t
he
Cou
ntr
y P
antr
y,cu
stom
ers
can
ch
oose
th
eir
eggs
scr
amb
led
,fri
ed,o
r p
oach
ed,w
hol
e w
hea
t or
wh
ite
toas
t,an
d e
ith
er o
ran
ge,a
pp
le,t
omat
o,or
gra
pef
ruit
ju
ice.
How
man
y d
iffe
ren
tB
reak
fast
Sp
ecia
ls c
an a
cu
stom
er o
rder
?A
cu
stom
er’s
ch
oice
of
eggs
doe
s n
ot a
ffec
t h
is o
r h
er c
hoi
ce o
f to
ast
or ju
ice,
so t
he
even
tsar
e in
depe
nde
nt.
Th
ere
are
3 w
ays
to c
hoo
se e
ggs,
2 w
ays
to c
hoo
se t
oast
,an
d 4
way
s to
choo
se ju
ice.
By
the
Fu
nda
men
tal
Cou
nti
ng
Pri
nci
ple,
ther
e ar
e 3
�2
�4
or 2
4 w
ays
toch
oose
th
e B
reak
fast
Spe
cial
.
Sol
ve e
ach
pro
ble
m.
1.T
he
Pal
ace
of P
izza
off
ers
smal
l,m
ediu
m,o
r la
rge
pizz
as w
ith
14
diff
eren
t to
ppin
gsav
aila
ble.
How
man
y di
ffer
ent
one-
topp
ing
pizz
as d
o th
ey s
erve
?42
2.T
he
lett
ers
A,B
,C,a
nd
D a
re u
sed
to f
orm
fou
r-le
tter
pas
swor
ds f
or e
nte
rin
g a
com
pute
rfi
le.H
ow m
any
pass
wor
ds a
re p
ossi
ble
if l
ette
rs c
an b
e re
peat
ed?
256
3.A
res
tau
ran
t se
rves
5 m
ain
dis
hes
,3 s
alad
s,an
d 4
dess
erts
.How
man
y di
ffer
ent
mea
lsco
uld
be
orde
red
if e
ach
has
a m
ain
dis
h,a
sal
ad,a
nd
a de
sser
t?60
4.M
aris
sa b
rou
ght
8 T-
shir
ts a
nd
6 pa
irs
of s
hor
ts t
o su
mm
er c
amp.
How
man
y di
ffer
ent
outf
its
con
sist
ing
of a
T-s
hir
t an
d a
pair
of
shor
ts d
oes
she
hav
e?48
5.T
her
e ar
e 6
diff
eren
t pa
ckag
es a
vail
able
for
sch
ool
pict
ure
s.T
he
stu
dio
offe
rs 5
dif
fere
nt
back
grou
nds
an
d 2
diff
eren
t fi
nis
hes
.How
man
y di
ffer
ent
opti
ons
are
avai
labl
e?60
6.H
ow m
any
5-di
git
even
nu
mbe
rs c
an b
e fo
rmed
usi
ng
the
digi
ts 4
,6,7
,2,8
if
digi
ts c
anbe
rep
eate
d?25
00
7.H
ow m
any
lice
nse
pla
te n
um
bers
con
sist
ing
of t
hre
e le
tter
s fo
llow
ed b
y th
ree
nu
mbe
rsar
e po
ssib
le w
hen
rep
etit
ion
is
allo
wed
?17
,576
,000
8.H
ow m
any
4-di
git
posi
tive
eve
n i
nte
gers
are
th
ere?
4500
Exam
ple
Exam
ple
Exer
cises
Exer
cises
©G
lenc
oe/M
cGra
w-H
ill70
0G
lenc
oe A
lgeb
ra 2
Dep
end
ent
Even
tsIf
th
e ou
tcom
e of
an
eve
nt
doe
saf
fect
th
e ou
tcom
e of
an
oth
er e
ven
t,th
e tw
o ev
ents
are
sai
d to
be
dep
end
ent.
The
Fun
dam
enta
l C
ount
ing
Pri
ncip
le s
till
app
lies
.
ENTE
RTA
INM
ENT
Th
e gu
ests
at
a sl
eep
over
bro
ugh
t 8
vid
eos.
Th
eyd
ecid
ed t
hey
wou
ld o
nly
wat
ch 3
vid
eos.
How
man
y or
der
s of
3 d
iffe
ren
t vi
deo
sar
e p
ossi
ble
?A
fter
th
e gr
oup
choo
ses
to w
atch
a v
ideo
,th
ey w
ill
not
ch
oose
to
wat
ch i
t ag
ain
,so
the
choi
ces
of v
ideo
s ar
e de
pen
den
t ev
ents
.
Th
ere
are
8 ch
oice
s fo
r th
e fi
rst
vide
o.T
hat
lea
ves
7 ch
oice
s fo
r th
e se
con
d.A
fter
th
ey c
hoo
seth
e fi
rst
2 vi
deos
,th
ere
are
6 re
mai
nin
g ch
oice
s.T
hu
s by
th
e F
un
dam
enta
l C
oun
tin
gP
rin
cipl
e,th
ere
are
8 �
7 �
6 or
336
ord
ers
of 3
dif
fere
nt
vide
os.
Sol
ve e
ach
pro
ble
m.
1.T
hre
e st
ude
nts
are
sch
edu
led
to g
ive
oral
rep
orts
on
Mon
day.
In h
ow m
any
way
s ca
nth
eir
pres
enta
tion
s be
ord
ered
?6
2.In
how
man
y w
ays
can
th
e fi
rst
five
let
ters
of
the
alph
abet
be
arra
nge
d if
eac
h l
ette
r is
use
d on
ly o
nce
?12
0
3.In
how
man
y di
ffer
ent
way
s ca
n 4
dif
fere
nt
book
s be
arr
ange
d on
th
e sh
elf?
24
4.H
ow m
any
lice
nse
pla
tes
con
sist
ing
of t
hre
e le
tter
s fo
llow
ed b
y th
ree
nu
mbe
rs a
repo
ssib
le w
hen
no
repe
titi
on i
s al
low
ed?
11,2
32,0
00
5.S
ixte
en t
eam
s ar
e co
mpe
tin
g in
a s
occe
r m
atch
.Gol
d,si
lver
,an
d br
onze
med
als
wil
l be
awar
ded
to t
he t
op t
hree
fin
ishe
rs.I
n ho
w m
any
way
s ca
n th
e m
edal
s be
aw
arde
d?33
60
6.In
a w
ord-
buil
din
g ga
me
each
pla
yer
pick
s 7
lett
er t
iles
.If
Juli
o’s
lett
ers
are
all
diff
eren
t,h
ow m
any
3-le
tter
com
bin
atio
ns
can
he
mak
e ou
t of
his
7 l
ette
rs?
210
7.T
he e
dito
r ha
s ac
cept
ed 6
art
icle
s fo
r th
e ne
ws
lett
er.I
n ho
w m
any
way
s ca
n th
e 6
arti
cles
be o
rder
ed?
720
8.T
her
e ar
e 10
on
e-h
our
wor
ksh
ops
sch
edu
led
for
the
open
hou
se a
t th
e gr
een
hou
se.
Th
ere
is o
nly
on
e co
nfe
ren
ce r
oom
ava
ilab
le.I
n h
ow m
any
way
s ca
n t
he
wor
ksh
ops
beor
dere
d?3,
628,
800
9.T
he
top
5 ru
nn
ers
at t
he
cros
s-co
un
try
mee
t w
ill
rece
ive
trop
hie
s.If
th
ere
are
22 r
un
ner
sin
th
e ra
ce,i
n h
ow m
any
way
s ca
n t
he
trop
hie
s be
aw
arde
d?3,
160,
080
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Th
e C
ou
nti
ng
Pri
nci
ple
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-1
12-1
Exam
ple
Exam
ple
Exer
cises
Exer
cises
© Glencoe/McGraw-Hill A3 Glencoe Algebra 2
An
swer
s
Answers (Lesson 12-1)
Skil
ls P
ract
ice
Th
e C
ou
nti
ng
Pri
nci
ple
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-1
12-1
©G
lenc
oe/M
cGra
w-H
ill70
1G
lenc
oe A
lgeb
ra 2
Lesson 12-1
Sta
te w
het
her
th
e ev
ents
are
in
dep
end
ent
or d
epen
den
t.
1.fi
nis
hin
g in
fir
st,s
econ
d,or
th
ird
plac
e in
a t
en-p
erso
n r
ace
dep
end
ent
2.ch
oosi
ng
a pi
zza
size
an
d a
topp
ing
for
the
pizz
ain
dep
end
ent
3.S
even
ty-f
ive
raff
le t
icke
ts a
re p
lace
d in
a ja
r.T
hre
e ti
cket
s ar
e th
en s
elec
ted,
one
afte
rth
e ot
her
,wit
hou
t re
plac
ing
a ti
cket
aft
er i
t is
ch
osen
.d
epen
den
t
4.T
he
232
mem
bers
of
the
fres
hm
an c
lass
all
vot
e by
sec
ret
ball
ot f
or t
he
clas
sre
pres
enta
tive
to
the
Stu
den
t S
enat
e.in
dep
end
ent
Sol
ve e
ach
pro
ble
m.
5.A
su
rvey
ing
firm
pla
ns
to b
uy
a co
lor
prin
ter
for
prin
tin
g it
s m
aps.
It h
as n
arro
wed
its
choi
ce t
o on
e of
th
ree
mod
els.
Eac
h o
f th
e m
odel
s is
ava
ilab
le w
ith
eit
her
32
meg
abyt
esof
ran
dom
acc
ess
mem
ory
(RA
M),
64 m
egab
ytes
of
RA
M,o
r 12
8 m
egab
ytes
of
RA
M.
Fro
m h
ow m
any
com
bin
atio
ns
of m
odel
s an
d R
AM
doe
s th
e fi
rm h
ave
to c
hoo
se?
9
6.H
ow m
any
arra
nge
men
ts o
f th
ree
lett
ers
can
be
form
ed f
rom
th
e le
tter
s of
th
e w
ord
MA
TH
if a
ny
lett
er w
ill
not
be
use
d m
ore
than
on
ce?
24
7.A
llan
is
play
ing
the
role
of
Oli
ver
in h
is s
choo
l’s p
rodu
ctio
n o
f O
live
r T
wis
t.T
he
war
drob
e cr
ew h
as p
rese
nte
d A
llan
wit
h 5
pai
rs o
f pa
nts
an
d 4
shir
ts t
hat
he
can
wea
r.H
ow m
any
poss
ible
cos
tum
es c
onsi
stin
g of
a p
air
of p
ants
an
d a
shir
t do
es A
llan
hav
e to
choo
se f
rom
?20
8.T
he 1
0-m
embe
r st
eeri
ng c
omm
itte
e th
at i
s pr
epar
ing
a st
udy
of t
he p
ubli
c tr
ansp
orta
tion
nee
ds o
f it
s to
wn
wil
l se
lect
a c
hai
rper
son
,vic
e-ch
airp
erso
n,a
nd
secr
etar
y fr
om t
he
com
mit
tee.
No
pers
on c
an s
erve
in
mor
e th
an o
ne
posi
tion
.In
how
man
y w
ays
can
th
eth
ree
posi
tion
s be
fil
led?
720
9.Je
anin
e h
as d
ecid
ed t
o bu
y a
pick
up
tru
ck.H
er c
hoi
ces
incl
ude
eit
her
a V
-6 e
ngi
ne
or a
V-8
en
gin
e,a
stan
dard
cab
or
an e
xten
ded
cab,
and
2-w
hee
l dr
ive
or 4
-wh
eel
driv
e.H
owm
any
poss
ible
mod
els
does
sh
e h
ave
to c
hoo
se f
rom
?8
10.A
mai
l-or
der
com
pan
y th
at s
ells
gar
den
ing
tool
s of
fers
rak
es i
n t
wo
diff
eren
t le
ngt
hs.
Cu
stom
ers
can
als
o ch
oose
eit
her
a w
oode
n,p
last
ic,o
r fi
berg
lass
han
dle
for
the
rake
.H
ow m
any
diff
eren
t ki
nds
of
rake
s ca
n a
cu
stom
er b
uy?
6
11.A
Mex
ican
res
tau
ran
t of
fers
ch
icke
n,b
eef,
or v
eget
aria
n f
ajit
as w
rapp
ed w
ith
eit
her
cor
nor
flo
ur
tort
illa
s,an
d to
pped
wit
h e
ith
er m
ild,
med
ium
,or
hot
sal
sa.H
ow m
any
diff
eren
tch
oice
s of
faj
itas
doe
s a
cust
omer
hav
e?18
©G
lenc
oe/M
cGra
w-H
ill70
2G
lenc
oe A
lgeb
ra 2
Sta
te w
het
her
th
e ev
ents
are
in
dep
end
ent
or d
epen
den
t.
1.ch
oosi
ng
an i
ce c
ream
fla
vor
and
choo
sin
g a
topp
ing
for
the
ice
crea
min
dep
end
ent
2.ch
oosi
ng
an o
ffen
sive
pla
yer
of t
he
gam
e an
d a
defe
nsi
ve p
laye
r of
th
e ga
me
in a
prof
essi
onal
foo
tbal
l ga
me
ind
epen
den
t
3.F
rom
15
entr
ies
in a
n a
rt c
onte
st,a
cam
p co
un
selo
r ch
oose
s fi
rst,
seco
nd,
and
thir
d pl
ace
win
ner
s.d
epen
den
t
4.Ji
llia
n i
s se
lect
ing
two
mor
e co
urs
es f
or h
er b
lock
sch
edu
le n
ext
sem
este
r.S
he
mu
stse
lect
on
e of
th
ree
mor
nin
g h
isto
ry c
lass
es a
nd
one
of t
wo
afte
rnoo
n m
ath
cla
sses
.in
dep
end
ent
Sol
ve e
ach
pro
ble
m.
5.A
bri
efca
se l
ock
has
3 r
otat
ing
cyli
nde
rs,e
ach
con
tain
ing
10 d
igit
s.H
ow m
any
nu
mer
ical
code
s ar
e po
ssib
le?
1000
6.A
gol
f cl
ub
man
ufa
ctu
rer
mak
es i
ron
s w
ith
7 d
iffe
ren
t sh
aft
len
gth
s,3
diff
eren
t gr
ips,
5di
ffer
ent
lies
,an
d 2
diff
eren
t cl
ub
hea
d m
ater
ials
.How
man
y di
ffer
ent
com
bin
atio
ns
are
offe
red?
210
7.T
her
e ar
e fi
ve d
iffe
ren
t ro
ute
s th
at a
com
mu
ter
can
tak
e fr
om h
er h
ome
to t
he
offi
ce.I
nh
ow m
any
way
s ca
n s
he
mak
e a
rou
nd
trip
if
she
use
s a
diff
eren
t ro
ute
com
ing
than
goin
g?20
8.In
how
man
y w
ays
can
th
e fo
ur
call
let
ters
of
a ra
dio
stat
ion
be
arra
nge
d if
th
e fi
rst
lett
er m
ust
be
W o
r K
an
d n
o le
tter
s re
peat
?27
,600
9.H
ow m
any
7-di
git
phon
e n
um
bers
can
be
form
ed i
f th
e fi
rst
digi
t ca
nn
ot b
e 0
or 1
,an
dan
y di
git
can
be
repe
ated
?8,
000,
000
10.H
ow m
any
7-di
git
phon
e n
um
bers
can
be
form
ed i
f th
e fi
rst
digi
t ca
nn
ot b
e 0,
and
any
digi
t ca
n b
e re
peat
ed?
9,00
0,00
0
11.H
ow m
any
7-di
git
phon
e n
um
bers
can
be
form
ed i
f th
e fi
rst
digi
t ca
nn
ot b
e 0
or 1
,an
d if
no
digi
t ca
n b
e re
peat
ed?
483,
840
12.H
ow m
any
7-di
git
phon
e n
um
bers
can
be
form
ed i
f th
e fi
rst
digi
t ca
nn
ot b
e 0,
and
if n
odi
git
can
be
repe
ated
?54
4,32
0
13.H
ow m
any
6-ch
arac
ter
pass
wor
ds c
an b
e fo
rmed
if
the
firs
t ch
arac
ter
is a
dig
it a
nd
the
rem
ain
ing
5 ch
arac
ters
are
let
ters
th
at c
an b
e re
peat
ed?
118,
813,
760
14.H
ow m
any
6-ch
arac
ter
pass
wor
ds c
an b
e fo
rmed
if
the
firs
t an
d la
st c
har
acte
rs a
redi
gits
an
d th
e re
mai
nin
g ch
arac
ters
are
let
ters
? A
ssu
me
that
an
y ch
arac
ter
can
be
repe
ated
.45
,697
,600
Pra
ctic
e (
Ave
rag
e)
Th
e C
ou
nti
ng
Pri
nci
ple
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-1
12-1
© Glencoe/McGraw-Hill A4 Glencoe Algebra 2
Answers (Lesson 12-1)
Readin
g t
o L
earn
Math
em
ati
csT
he
Co
un
tin
g P
rin
cip
le
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-1
12-1
©G
lenc
oe/M
cGra
w-H
ill70
3G
lenc
oe A
lgeb
ra 2
Lesson 12-1
Pre-
Act
ivit
yH
ow c
an y
ou c
oun
t th
e m
axim
um
nu
mb
er o
f li
cen
se p
late
s a
stat
eca
n i
ssu
e?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 12
-1 a
t th
e to
p of
pag
e 63
2 in
you
r te
xtbo
ok.
Ass
um
e th
at a
ll F
lori
da l
icen
se p
late
s h
ave
thre
e le
tter
s fo
llow
ed b
y th
ree
digi
ts,a
nd
that
th
ere
are
no
rule
s ag
ain
st u
sin
g th
e sa
me
lett
er o
r n
um
ber
mor
e th
an o
nce
.How
man
y ch
oice
s ar
e th
ere
for
each
let
ter?
for
eac
h d
igit
?26
;10
Rea
din
g t
he
Less
on
1.S
ham
im i
s si
gnin
g u
p fo
r h
er c
lass
es.M
ost
of h
er c
lass
es a
re r
equ
ired
,bu
t sh
e h
as t
wo
elec
tive
s.F
or h
er a
rts
clas
s,sh
e ca
n c
hos
e be
twee
n A
rt,B
and,
Ch
oru
s,or
Dra
ma.
For
her
lan
guag
e cl
ass,
she
can
ch
oose
bet
wee
n F
ren
ch,G
erm
an,a
nd
Spa
nis
h.
a.T
o or
gan
ize
her
ch
oice
s,S
ham
im d
ecid
es t
o m
ake
a tr
ee d
iagr
am.L
et A
,B,C
,an
d D
repr
esen
t A
rt,B
and,
Ch
oru
s,an
d D
ram
a,an
d F,
G,a
nd
S r
epre
sen
t F
ren
ch,G
erm
an,
and
Spa
nis
h.C
ompl
ete
the
foll
owin
g di
agra
m.
b.
How
cou
ld S
ham
im h
ave
foun
d th
e nu
mbe
r of
pos
sibl
e co
mbi
nati
ons
wit
hout
mak
ing
atr
ee d
iagr
am?
Sam
ple
an
swer
:Mu
ltip
ly t
he
nu
mb
er o
f ch
oic
es f
or
her
art
scl
ass
by t
he
nu
mb
er o
f ch
oic
es f
or
her
lan
gu
age
clas
s:3
�4
�12
.
2.A
jar
con
tain
s 6
red
mar
bles
,4 b
lue
mar
bles
,an
d 3
yell
ow m
arbl
es.I
ndi
cate
wh
eth
er t
he
even
ts d
escr
ibed
are
dep
end
ent
or i
nd
epen
den
t.
a.A
mar
ble
is d
raw
n o
ut
of t
he
jar
and
is n
ot r
epla
ced.
A s
econ
d m
arbl
e is
dra
wn
.d
epen
den
t
b.
A m
arbl
e is
dra
wn
ou
t of
th
e ja
r an
d is
pu
t ba
ck i
n.T
he
jar
is s
hak
en.A
sec
ond
mar
ble
is d
raw
n.
ind
epen
den
t
Hel
pin
g Y
ou
Rem
emb
er
3.O
ne
defi
nit
ion
of
ind
epen
den
tis
“n
ot d
eter
min
ed o
r in
flu
ence
d by
som
eon
e or
som
eth
ing
else
.”H
ow c
an t
his
def
init
ion
hel
p yo
u r
emem
ber
the
diff
eren
ce b
etw
een
in
dep
end
ent
and
dep
end
ent
even
ts?
Sam
ple
an
swer
:If
th
e o
utc
om
e o
f o
ne
even
t d
oes
no
taf
fect
or
infl
uen
ce t
he
ou
tco
me
of
ano
ther
,th
e ev
ents
are
ind
epen
den
t.If
the
ou
tco
me
of
on
e ev
ent
do
esaf
fect
or
infl
uen
ce t
he
ou
tco
me
of
ano
ther
,th
e ev
ents
are
dep
end
ent.
FGA
S
AF
AG
AS
FGB
S
BF
BG
BS
FGC
S
CF
CG
CS
FGD
S
DF
DG
DS
©G
lenc
oe/M
cGra
w-H
ill70
4G
lenc
oe A
lgeb
ra 2
Tree
Dia
gra
ms
and
th
e P
ow
er R
ule
If y
ou f
lip
a co
in o
nce
,th
ere
are
two
poss
ible
ou
tcom
es:h
eads
sh
owin
g (H
) or
tai
ls s
how
ing
(T).
Th
e tr
ee d
iagr
am t
o th
e ri
ght
show
s th
e fo
ur
(22 )
poss
ible
ou
tcom
es i
f yo
u f
lip
a co
in t
wic
e.
Flip
2
H T H T
Flip
1
H T
Ou
tco
mes
HH
HT
TH TT
star
t
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-1
12-1
Dra
w a
tre
e d
iagr
am t
osh
ow a
ll t
he
pos
sib
le o
utc
omes
for
fli
pp
ing
a co
in t
hre
e ti
mes
.Lis
t th
e ou
tcom
es.
Th
ere
are
eigh
t (2
3 ) p
ossi
ble
outc
omes
.Wit
hea
ch e
xtra
fli
p,th
e n
um
ber
of o
utc
omes
do
ubl
es.W
ith
4 f
lips
,th
ere
wou
ld b
e si
xtee
n(2
4 ) o
utc
omes
.
Flip
2
H T H T
Flip
1
H T
Flip
3
H T H T H T H T
Ou
tco
mes
HH
HH
HT
HT
HH
TT
TH
HT
HT
TT
HT
TT
star
t
In a
cu
p t
her
e ar
e a
red
,a b
lue,
and
a y
ello
w m
arb
le.H
owm
any
pos
sib
le o
utc
omes
are
th
ere
ifyo
u d
raw
on
e m
arb
le a
t ra
nd
om,
rep
lace
it,
and
th
en d
raw
an
oth
er?
Th
ere
are
nin
e (3
2 ) p
ossi
ble
outc
omes
.
Dra
w 2
R B Y R B Y R B Y
Ou
tco
mes
RR
RB
RY
BR
BB
BY
YR
YB
YY
Dra
w 1
R B Y
star
t
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Th
e P
ower
Ru
le f
or t
he
nu
mbe
r of
ou
tcom
es s
tate
s th
at i
f an
exp
erim
ent
isre
peat
ed n
tim
es,a
nd
if t
her
e ar
e b
poss
ible
ou
tcom
es e
ach
tim
e,th
ere
are
bnto
tal
poss
ible
ou
tcom
es.
Fin
d t
he
tota
l n
um
ber
of
pos
sib
le o
utc
omes
for
eac
h e
xper
imen
t.U
setr
ee d
iagr
ams
to h
elp
you
.
1.fl
ippi
ng
a co
in 5
tim
es25
2.do
ing
the
mar
ble
expe
rim
ent
6 ti
mes
36
3.fl
ippi
ng
a co
in 8
tim
es28
4.ro
llin
g a
6-si
ded
die
2 ti
mes
62
5.ro
llin
g a
6-si
ded
die
3 ti
mes
636.
roll
ing
a 4-
side
d di
e 2
tim
es42
7.ro
llin
g a
4-si
ded
die
3 ti
mes
438.
roll
ing
a 12
-sid
ed d
ie 2
tim
es12
2
© Glencoe/McGraw-Hill A5 Glencoe Algebra 2
An
swer
s
Answers (Lesson 12-2)
Stu
dy G
uid
e a
nd I
nte
rven
tion
Per
mu
tati
on
s an
d C
om
bin
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-2
12-2
©G
lenc
oe/M
cGra
w-H
ill70
5G
lenc
oe A
lgeb
ra 2
Lesson 12-2
Perm
uta
tio
ns
Wh
en a
gro
up
of o
bjec
ts o
r pe
ople
are
arr
ange
d in
a c
erta
in o
rder
,th
ear
ran
gem
ent
is c
alle
d a
per
mu
tati
on.
Per
mu
tati
on
sT
he n
umbe
r of
per
mut
atio
ns o
f ndi
stin
ct o
bjec
ts ta
ken
rat
a ti
me
is g
iven
by
P(n
, r)
�.
Per
mu
tati
on
s w
ith
Rep
etit
ion
sT
he n
umbe
r of
per
mut
atio
ns o
f n
obje
cts
of w
hich
par
e al
ike
and
qar
e al
ike
is
.
Th
e ru
le f
or p
erm
uta
tion
s w
ith
rep
etit
ion
s ca
n b
e ex
ten
ded
to a
ny
nu
mbe
r of
obj
ects
th
atar
e re
peat
ed.
Fro
m a
lis
t of
20
boo
ks,
each
stu
den
t m
ust
ch
oose
4 b
ook
s fo
r b
ook
rep
orts
.Th
e fi
rst
rep
ort
is a
tra
dit
ion
al b
ook
rep
ort,
the
seco
nd
a p
oste
r,th
e th
ird
a n
ewsp
aper
in
terv
iew
wit
h o
ne
of t
he
char
acte
rs,a
nd
th
e fo
urt
h a
tim
elin
e of
th
ep
lot.
How
man
y d
iffe
ren
t or
der
ings
of
boo
ks
can
be
chos
en?
Sin
ce e
ach
boo
k re
port
has
a d
iffe
ren
t fo
rmat
,ord
er i
s im
port
ant.
You
mu
st f
ind
the
nu
mbe
rof
per
mu
tati
ons
of 2
0 ob
ject
s ta
ken
4 a
t a
tim
e.
P(n
,r)
�P
erm
utat
ion
form
ula
P(2
0,4)
�n
�20
, r
�4
�S
impl
ify.
�D
ivid
e by
com
mon
fac
tors
.
�11
6,28
0B
ooks
for
th
e bo
ok r
epor
ts c
an b
e ch
osen
116
,280
way
s.
Eva
luat
e ea
ch e
xpre
ssio
n.
1.P
(6,3
)12
02.
P(8
,5)
6720
3.P
(9,4
)30
244.
P(1
1,6)
332,
640
How
man
y d
iffe
ren
t w
ays
can
th
e le
tter
s of
eac
h w
ord
be
arra
nge
d?
5.M
OM
36.
MO
ND
AY
720
7.S
TE
RE
O36
0
8.SC
HO
OL
Th
e h
igh
sch
ool
chor
us
has
bee
n p
ract
icin
g 12
son
gs,b
ut
ther
e is
tim
e fo
r on
ly5
of t
hem
at
the
spri
ng
con
cert
.How
may
dif
fere
nt
orde
rin
gs o
f 5
son
gs a
re p
ossi
ble?
95,0
40
20 �
19 �
18 �
17 �
16 �
15 �
… �
1�
��
�16
�15
�…
�1
20!
� 16!20
!�
�(2
0 �
4)!
n!
� (n�
r)!
n!
� p!q
!
n!
� (n�
r)!
Exam
ple
Exam
ple
Exer
cises
Exer
cises
11
1
11
1
©G
lenc
oe/M
cGra
w-H
ill70
6G
lenc
oe A
lgeb
ra 2
Co
mb
inat
ion
sA
n a
rran
gem
ent
or s
elec
tion
of
obje
cts
in w
hic
h o
rder
is
not
impo
rtan
t is
call
ed a
com
bin
atio
n.
Co
mb
inat
ion
sT
he n
umbe
r of
com
bina
tions
of n
dist
inct
obj
ects
take
n r
at a
tim
e is
giv
en b
y C
(n, r
) �
.
SCH
OO
LH
ow m
any
grou
ps
of 4
stu
den
ts c
an b
e se
lect
ed f
rom
acl
ass
of 2
0?S
ince
th
e or
der
of c
hoo
sin
g th
e st
ude
nts
is
not
im
port
ant,
you
mu
st f
ind
the
nu
mbe
r of
com
bin
atio
ns
of 2
0 st
ude
nts
tak
en 4
at
a ti
me.
C(n
,r)
�C
ombi
natio
n fo
rmul
a
C(2
0,4)
�n
�20
, r
�4
�or
484
5
Th
ere
are
4845
pos
sibl
e w
ays
to c
hoo
se 4
stu
den
ts.
In h
ow m
any
way
s ca
n y
ou c
hoo
se 1
vow
el a
nd
2 c
onso
nan
ts f
rom
ase
t of
26
lett
er t
iles
? (A
ssu
me
ther
e ar
e 5
vow
els
and
21
con
son
ants
.)B
y th
e F
un
dam
enta
l C
oun
tin
g P
rin
cipl
e,yo
u c
an m
ult
iply
th
e n
um
ber
of w
ays
to s
elec
t on
evo
wel
an
d th
e n
um
ber
of w
ays
to s
elec
t 2
con
son
ants
.On
ly t
he
lett
ers
chos
en m
atte
r,n
otth
e or
der
in w
hic
h t
hey
wer
e ch
osen
,so
use
com
bin
atio
ns.
C(5
,1)
On
e of
5 v
owel
s ar
e dr
awn
.C
(21,
2)T
wo
of 2
1 co
nso
nan
ts a
re d
raw
n.
C(5
,1)
�C
(21,
2) �
�C
ombi
natio
n fo
rmul
a
��
Sub
trac
t.
�5
�21
0 or
105
0S
impl
ify.
Th
ere
are
1050
com
bin
atio
ns
of 1
vow
el a
nd
2 co
nso
nan
ts.
Eva
luat
e ea
ch e
xpre
ssio
n.
1.C
(5,3
)10
2.C
(7,4
)35
3.C
(15,
7)64
354.
C(1
0,5)
252
5.PL
AY
ING
CA
RD
SF
rom
a s
tan
dard
dec
k of
52
card
s,in
how
man
y w
ays
can
5 c
ards
be
draw
n?
2,59
8,96
0
6.H
OC
KEY
How
man
y h
ocke
y te
ams
of 6
pla
yers
can
be
form
ed f
rom
14
play
ers
wit
hou
tre
gard
to
posi
tion
pla
yed?
3003
7.C
OM
MIT
TEES
Fro
m a
gro
up
of 1
0 m
en a
nd
12 w
omen
,how
man
y co
mm
itte
es o
f 5
men
and
6 w
omen
can
be
form
ed?
232,
848
21!
� 19!2
!5! � 4!
21!
��
(21
�2)
!2!
5!�
�(5
�1)
!1!
20!
� 16!4
!20!
��
(20
�4)
!4!
n!
��
(n�
r)!r
!
n!
��
(n�
r)!r
!
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Per
mu
tati
on
s an
d C
om
bin
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-2
12-2
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
© Glencoe/McGraw-Hill A6 Glencoe Algebra 2
Answers (Lesson 12-2)
Skil
ls P
ract
ice
Per
mu
tati
on
s an
d C
om
bin
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-2
12-2
©G
lenc
oe/M
cGra
w-H
ill70
7G
lenc
oe A
lgeb
ra 2
Lesson 12-2
Eva
luat
e ea
ch e
xpre
ssio
n.
1.P
(6,3
)12
02.
P(8
,2)
563.
P(2
,1)
2
4.P
(3,2
)6
5.P
(10,
4)50
406.
P(5
,5)
120
7.C
(2,2
)1
8.C
(5,3
)10
9.C
(4,1
)4
10.C
(8,7
)8
11.C
(3,2
)3
12.C
(7,4
)35
Det
erm
ine
wh
eth
er e
ach
sit
uat
ion
in
volv
es a
per
mu
tati
onor
a c
ombi
na
tion
.Th
enfi
nd
th
e n
um
ber
of
pos
sib
ilit
ies.
13.s
eati
ng
8 st
ude
nts
in
8 s
eats
in
th
e fr
ont
row
of
the
sch
ool
audi
tori
um
per
mu
tati
on
;40
,320
14.i
ntr
odu
cin
g th
e 5
star
tin
g pl
ayer
s on
th
e W
oods
vill
e H
igh
Sch
ool
bask
etba
ll t
eam
at
the
begi
nn
ing
of t
he
nex
t ba
sket
ball
gam
ep
erm
uta
tio
n;
120
15.c
hec
kin
g ou
t 3
libr
ary
book
s fr
om a
lis
t of
8 b
ooks
for
a r
esea
rch
pap
erco
mb
inat
ion
;56
16.c
hoo
sin
g 2
mov
ies
to r
ent
from
5 m
ovie
sco
mb
inat
ion
;10
17.t
he
firs
t-,s
econ
d-,a
nd
thir
d-pl
ace
fin
ish
ers
in a
rac
e w
ith
10
con
test
ants
per
mu
tati
on
;72
0
18.e
lect
ing
4 ca
ndi
date
s to
a m
un
icip
al p
lan
nin
g bo
ard
from
a f
ield
of
7 ca
ndi
date
sco
mb
inat
ion
;35
19.c
hoo
sin
g 2
vege
tabl
es f
rom
a m
enu
th
at o
ffer
s 6
vege
tabl
e ch
oice
sco
mb
inat
ion
;15
20.a
n a
rran
gem
ent
of t
he
lett
ers
in t
he
wor
d rh
ombu
sp
erm
uta
tio
n;
5040
21.s
elec
tin
g 2
of 8
ch
oice
s of
ora
nge
juic
e at
a s
tore
com
bin
atio
n;
28
22.p
laci
ng
a re
d ro
se b
ush
,a y
ello
w r
ose
bush
,a w
hit
e ro
se b
ush
,an
d a
pin
k ro
se b
ush
in
aro
w i
n a
pla
nte
rp
erm
uta
tio
n;
24
23.s
elec
tin
g 2
of 9
kit
ten
s at
an
an
imal
res
cue
shel
ter
com
bin
atio
n;
36
24.a
n a
rran
gem
ent
of t
he
lett
ers
in t
he
wor
d is
osce
les
per
mu
tati
on
;30
,240
©G
lenc
oe/M
cGra
w-H
ill70
8G
lenc
oe A
lgeb
ra 2
Eva
luat
e ea
ch e
xpre
ssio
n.
1.P
(8,6
)20
,160
2.P
(9,7
)18
1,44
03.
P(3
,3)
6
4.P
(4,3
)24
5.P
(4,1
)4
6.P
(7,2
)42
7.C
(8,2
)28
8.C
(11,
3)16
59.
C(2
0,18
)19
0
10.C
(9,9
)1
11.C
(3,1
)3
12.C
(9,3
) �
C(6
,2)
1260
Det
erm
ine
wh
eth
er e
ach
sit
uat
ion
in
volv
es a
per
mu
tati
onor
a c
ombi
na
tion
.Th
enfi
nd
th
e n
um
ber
of
pos
sib
ilit
ies.
13.s
elec
tin
g a
4-pe
rson
bob
sled
tea
m f
rom
a g
rou
p of
9 a
thle
tes
com
bin
atio
n;
126
14.a
n a
rran
gem
ent
of t
he
lett
ers
in t
he
wor
d C
anad
ap
erm
uta
tio
n;
120
15.a
rran
gin
g 4
char
ms
on a
bra
cele
t th
at h
as a
cla
sp,a
fro
nt,
and
a ba
ckp
erm
uta
tio
n;
24
16.s
elec
tin
g 3
dess
erts
fro
m 1
0 de
sser
ts t
hat
are
dis
play
ed o
n a
des
sert
car
t in
a r
esta
ura
nt
com
bin
atio
n;
120
17.a
n a
rran
gem
ent
of t
he
lett
ers
in t
he
wor
d an
nu
ally
per
mu
tati
on
;50
40
18.f
orm
ing
a 2-
pers
on s
ales
tea
m f
rom
a g
rou
p of
12
sale
speo
ple
com
bin
atio
n;
66
19.m
akin
g 5-
side
d po
lygo
ns b
y ch
oosi
ng a
ny 5
of
11 p
oint
s lo
cate
d on
a c
ircl
e to
be
the
vert
ices
com
bin
atio
n;
462
20.s
eati
ng
5 m
en a
nd
5 w
omen
alt
ern
atel
y in
a r
ow,b
egin
nin
g w
ith
a w
oman
per
mu
tati
on
;14
,400
21.S
TUD
ENT
GR
OU
PSFa
rmin
gton
Hig
h i
s pl
ann
ing
its
acad
emic
fes
tiva
l.A
ll m
ath
clas
ses
wil
l se
nd
2 re
pres
enta
tive
s to
com
pete
in
th
e m
ath
bow
l.H
ow m
any
diff
eren
tgr
oups
of
stu
den
ts c
an b
e ch
osen
fro
m a
cla
ss o
f 16
stu
den
ts?
120
22.P
HO
TOG
RA
PHY
A p
hot
ogra
pher
is
taki
ng
pict
ure
s of
a b
ride
an
d gr
oom
an
d th
eir
6at
ten
dan
ts.I
f sh
e ta
kes
phot
ogra
phs
of 3
peo
ple
in a
gro
up,
how
man
y di
ffer
ent
grou
psca
n s
he
phot
ogra
ph?
56
23.A
IRLI
NES
An
air
lin
e is
hir
ing
5 fl
igh
t at
ten
dan
ts.I
f 8
peop
le a
pply
for
th
e jo
b,h
owm
any
diff
eren
t gr
oups
of
5 at
ten
dan
ts c
an t
he
airl
ine
hir
e?56
24.S
UB
SCR
IPTI
ON
SA
sch
ool
libr
aria
n w
ould
lik
e to
bu
y su
bscr
ipti
ons
to 7
new
mag
azin
es.H
er b
udg
et,h
owev
er,w
ill
allo
w h
er t
o bu
y on
ly 4
new
su
bscr
ipti
ons.
How
man
y di
ffer
ent
grou
ps o
f 4
mag
azin
es c
an s
he
choo
se f
rom
th
e 7
mag
azin
es?
35
Pra
ctic
e (
Ave
rag
e)
Per
mu
tati
on
s an
d C
om
bin
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-2
12-2
© Glencoe/McGraw-Hill A7 Glencoe Algebra 2
An
swer
s
Answers (Lesson 12-2)
Readin
g t
o L
earn
Math
em
ati
csP
erm
uta
tio
ns
and
Co
mb
inat
ion
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-2
12-2
©G
lenc
oe/M
cGra
w-H
ill70
9G
lenc
oe A
lgeb
ra 2
Lesson 12-2
Pre-
Act
ivit
yH
ow d
o p
erm
uta
tion
s an
d c
omb
inat
ion
s ap
ply
to
soft
bal
l?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 12
-2 a
t th
e to
p of
pag
e 63
8 in
you
r te
xtbo
ok.
Su
ppos
e th
at 2
0 st
ude
nts
en
ter
a m
ath
con
test
.In
how
man
y w
ays
can
firs
t,se
con
d,an
d th
ird
plac
es b
e aw
arde
d? (
Wri
te y
our
answ
er a
s a
prod
uct
.D
o n
ot c
alcu
late
th
e pr
odu
ct.)
20 �
19 �
18
Rea
din
g t
he
Less
on
1.In
dica
te w
het
her
eac
h s
itu
atio
n i
nvo
lves
a p
erm
uta
tion
or a
com
bin
atio
n.
a.ch
oosi
ng
five
stu
den
ts f
rom
a c
lass
to
wor
k on
a s
peci
al p
roje
ctco
mb
inat
ion
b.
arra
ngi
ng
five
pic
ture
s in
a r
ow o
n a
wal
lp
erm
uta
tio
n
c.dr
awin
g a
han
d of
13
card
s fr
om a
52-
card
dec
kco
mb
inat
ion
d.
arra
ngi
ng
the
lett
ers
of t
he
wor
d al
gebr
ap
erm
uta
tio
n
2.W
rite
an
exp
ress
ion
th
at c
an b
e u
sed
to c
alcu
late
eac
h o
f th
e fo
llow
ing.
a.n
um
ber
of c
ombi
nat
ion
s of
ndi
stin
ct o
bjec
ts t
aken
rat
a t
ime� (n
�n! r)
!r!
�
b.
nu
mbe
r of
per
mu
tati
ons
of n
obje
cts
of w
hic
h p
are
alik
e an
d q
are
alik
e� pn !q! !
�
c.n
um
ber
of p
erm
uta
tion
s of
ndi
stin
ct o
bjec
ts t
aken
rat
a t
ime� (n
�n! r)
!�
3.F
ive
card
s ar
e dr
awn
fro
m a
sta
nda
rd d
eck
of c
ards
.Su
ppos
e yo
u a
re a
sked
to
dete
rmin
eh
ow m
any
poss
ible
han
ds c
onsi
st o
f on
e h
eart
,tw
o di
amon
ds,a
nd
two
spad
es.
a.W
hic
h o
f th
e fo
llow
ing
wou
ld y
ou u
se t
o so
lve
this
pro
blem
:Fu
nd
amen
tal
Cou
nti
ng
Pri
nci
ple,
perm
uta
tion
s,or
com
bin
atio
ns?
(M
ore
than
on
e of
th
ese
may
app
ly.)
Fu
nd
amen
tal C
ou
nti
ng
Pri
nci
ple
,co
mb
inat
ion
s
b.
Wri
te a
n ex
pres
sion
tha
t in
volv
es t
he n
otat
ion
P(n
,r)
and/
or C
(n,r
) th
at y
ou w
ould
use
to s
olve
th
is p
robl
em.(
Do
not
do
any
calc
ula
tion
s.)
C(1
3,1)
�C
(13,
2) �
C(1
3,2)
Hel
pin
g Y
ou
Rem
emb
er
4.M
any
stu
den
ts h
ave
trou
ble
know
ing
wh
en t
o u
se p
erm
uta
tion
s an
d w
hen
to
use
com
bin
atio
ns
to s
olve
cou
nti
ng
prob
lem
s.H
ow c
an t
he
idea
of
ord
erh
elp
you
to
rem
embe
r th
e di
ffer
ence
bet
wee
n p
erm
uta
tion
s an
d co
mbi
nat
ion
s?
Sam
ple
an
swer
:A
per
mu
tati
on
is a
n a
rran
gem
ent
of
ob
ject
s in
wh
ich
ord
er is
imp
ort
ant.
A c
om
bin
atio
n is
a s
elec
tio
n o
f o
bje
cts
in w
hic
h o
rder
is n
ot
imp
ort
ant.
©G
lenc
oe/M
cGra
w-H
ill71
0G
lenc
oe A
lgeb
ra 2
Co
mb
inat
ion
s an
d P
asca
l’s T
rian
gle
Pas
cal’s
tri
angl
e is
a s
peci
al a
rray
of
nu
mbe
rs i
nve
nte
d by
Bla
ise
Pas
cal
(162
3–16
62).
Th
e va
lues
in
Pas
cal’s
tri
angl
e ca
n b
e fo
un
d u
sin
g th
eco
mbi
nat
ion
s sh
own
bel
ow.
1.E
valu
ate
the
expr
essi
on i
n e
ach
cel
l of
th
e tr
ian
gle.
2.T
he p
atte
rn s
how
s th
e re
lati
onsh
ip b
etw
een
C(n
,r)
and
Pas
cal’s
tri
angl
e.In
gen
eral
,it
is t
rue
that
C(n
,r)
�C
(n,r
�1)
�C
(n�
1,r
�1)
.Com
plet
eth
e pr
oof
of t
his
pro
pert
y.In
eac
h s
tep,
the
den
omin
ator
has
bee
n g
iven
.
C(n
,r)
�C
(n,r
�1)
��
��
��
� � � � �C
(n�
1,r
�1)
(n�
1)!
(r�
1)![
(n�
1) �
(r�
1)]!
(n�
1)!
(r�
1)!(
n�
r)!
n!(
n�
1)(r
�1)
!(n
�r)
!
n!(
r�
1 �
n�
r)(r
�1)
!(n
�r)
!
n!(
n�
r)(r
�1)
!(n
�r)
!n
!(r
�1)
(r�
1)!(
n�
r)!
n!(
n�
r)(r
�1)
!(n
�r
�1)
!(n
�r)
n!(
r�
1)r!
(n�
r)!(
r�
1)
n!
(r�
1)!(
n�
r�
1)!
n!
r!(n
�r)
!
C(1
,0)
1
C(1
,1)
1C
(2,0
)
1
C(2
,1)
2
C(2
,2)
1
C(3
,0)
1
C(3
,1)
3
C(3
,2)
3
C(3
,3)
1C
(4,0
)
1
C(4
,1)
4
C(4
,2)
6
C(4
,3)
4
C(4
,4)
1
C(5
,0)
1
C(5
,1)
5
C(5
,2)
10
C(5
,3)
10
C(5
,4)
5
C(5
,5)
1
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-2
12-2
© Glencoe/McGraw-Hill A8 Glencoe Algebra 2
Answers (Lesson 12-3)
Stu
dy G
uid
e a
nd I
nte
rven
tion
Pro
bab
ility
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-3
12-3
©G
lenc
oe/M
cGra
w-H
ill71
1G
lenc
oe A
lgeb
ra 2
Lesson 12-3
Pro
bab
ility
an
d O
dd
sIn
pro
babi
lity
,a d
esir
ed o
utc
ome
is c
alle
d a
succ
ess;
any
oth
erou
tcom
e is
cal
led
a fa
ilu
re.
Pro
bab
ility
of
If an
eve
nt c
an s
ucce
ed in
sw
ays
and
fail
in f
way
s, t
hen
the
prob
abili
ties
of s
ucce
ss,
P(S
),
Su
cces
s an
dan
d of
fai
lure
, P
(F),
are
as
follo
ws.
Failu
reP
(S)
�an
d P
(F)
�.
Def
init
ion
If an
eve
nt c
an s
ucce
ed in
sw
ays
and
fail
in f
way
s, t
hen
the
odds
of
succ
ess
and
of f
ailu
re a
re
of
Od
ds
as f
ollo
ws.
Odd
s of
suc
cess
�s
:fO
dds
of f
ailu
re �
f:s
Wh
en 3
coi
ns
are
toss
ed,w
hat
is
the
pro
bab
ilit
y th
at a
t le
ast
2 ar
e h
ead
s?Yo
u c
an u
se a
tre
e di
agra
m t
o fi
nd
the
sam
ple
spac
e.O
f th
e 8
poss
ible
ou
tcom
es,4
hav
e at
lea
st 2
hea
ds.S
o th
e
prob
abil
ity
of t
ossi
ng
at l
east
2 h
eads
is
�4 8�or
�1 2� .
Wh
at i
s th
e p
rob
abil
ity
of p
ick
ing
4 fi
ctio
n b
ook
s an
d 2
bio
grap
hie
sfr
om a
bes
t-se
ller
lis
t th
at c
onsi
sts
of 1
2 fi
ctio
n b
ook
s an
d 6
bio
grap
hie
s?B
y th
e F
un
dam
enta
l C
oun
tin
g P
rin
cipl
e,th
e n
um
ber
of s
ucc
esse
s is
C(1
2,4)
�C
(6,2
).T
he
tota
l n
um
ber
of s
elec
tion
s,s
�f,
of 6
boo
ks i
s C
(18,
6).
P(4
fic
tion
,2 b
iogr
aph
y) �
or a
bou
t 0.
40
Th
e pr
obab
ilit
y of
sel
ecti
ng
4 fi
ctio
n b
ooks
an
d 2
biog
raph
ies
is a
bou
t 40
%.
Fin
d t
he
odd
s of
an
eve
nt
occu
rrin
g,gi
ven
th
e p
rob
abil
ity
of t
he
even
t.
1.�3 7�
3:4
2.�4 5�
4:1
3.� 12 3�
2:11
4.1:
14
Fin
d t
he
pro
bab
ilit
y of
an
eve
nt
occu
rrin
g,gi
ven
th
e od
ds
of t
he
even
t.
5.10
:1�1 10 1�
6.2:
5�2 7�
7.4:
9� 14 3�
8.8:
3� 18 1�
On
e b
ag o
f ca
nd
y co
nta
ins
15 r
ed c
and
ies,
10 y
ello
w c
and
ies,
and
6 g
reen
can
die
s.F
ind
th
e p
rob
abil
ity
of e
ach
sel
ecti
on.
9.pi
ckin
g a
red
can
dy�1 35 1�
10.n
ot p
icki
ng
a ye
llow
can
dy�2 31 1�
11.p
icki
ng
a gr
een
can
dy� 36 1�
12.n
ot p
icki
ng
a re
d ca
ndy
�1 36 1�
1 � 15
C(1
2,4)
�C
(6,2
)�
�C
(18,
6)
HH
HH
HT
HT
HH
TT
TH
HT
HT
TT
HT
TT
H T H T H T H T
H T
H T H T
Firs
tC
oin
Sec
ond
Co
inT
hird
Co
inP
oss
ible
Out
com
es
f� s
�f
s� s
�f
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
©G
lenc
oe/M
cGra
w-H
ill71
2G
lenc
oe A
lgeb
ra 2
Pro
bab
ility
Dis
trib
uti
on
sA
ran
dom
var
iab
leis
a v
aria
ble
wh
ose
valu
e is
th
en
um
eric
al o
utc
ome
of a
ran
dom
eve
nt.
A p
rob
abil
ity
dis
trib
uti
onfo
r a
part
icu
lar
ran
dom
vari
able
is
a fu
nct
ion
th
at m
aps
the
sam
ple
spac
e to
th
e pr
obab
ilit
ies
of t
he
outc
omes
in
th
esa
mpl
e sp
ace.
Su
pp
ose
two
dic
e ar
e ro
lled
.Th
e ta
ble
an
d t
he
rela
tive
-fre
qu
ency
his
togr
am s
how
th
e d
istr
ibu
tion
of
the
abso
lute
val
ue
of t
he
dif
fere
nce
of
the
nu
mb
ers
roll
ed.U
se t
he
grap
h t
o d
eter
min
e w
hic
h o
utc
ome
is t
he
mos
t li
kel
y.W
hat
is
its
pro
bab
ilit
y?
Th
e gr
eate
st p
roba
bili
ty i
n t
he
grap
h i
s �1 4� .
Th
e m
ost
like
ly o
utc
ome
is a
dif
fere
nce
of
1 an
d it
s
prob
abil
ity
is �1 4� .
Fou
r co
ins
are
toss
ed.
1.C
ompl
ete
the
tabl
e be
low
to
show
th
e pr
obab
ilit
y di
stri
buti
on o
f th
e n
um
ber
of h
eads
.
2.M
ake
rela
tive
-fre
quen
cy d
istr
ibu
tion
of
the
data
.
10
Hea
ds
Head
s in
Co
in T
oss
23
4
1 4
Probability
3 8 1 8 1 163 165 16Nu
mb
er o
f H
ead
s0
12
34
Pro
bab
ility
� 11 6��1 4�
�3 8��1 4�
� 11 6�
1 4
00
Probability
Dif
fere
nce
Nu
mb
ers
Sh
ow
ing
on
th
e D
ice
12
34
5
1 6 1 12
Dif
fere
nce
01
23
45
Pro
bab
ility
�1 6��1 4�
�1 6��1 6�
�1 6�� 11 2�
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Pro
bab
ility
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-3
12-3
Exam
ple
Exam
ple
Exer
cises
Exer
cises
© Glencoe/McGraw-Hill A9 Glencoe Algebra 2
An
swer
s
Answers (Lesson 12-3)
Skil
ls P
ract
ice
Pro
bab
ility
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-3
12-3
©G
lenc
oe/M
cGra
w-H
ill71
3G
lenc
oe A
lgeb
ra 2
Lesson 12-3
Ah
med
is
pos
tin
g 2
ph
otog
rap
hs
on h
is w
ebsi
te.H
e h
as n
arro
wed
his
ch
oice
s to
4la
nd
scap
e p
hot
ogra
ph
s an
d 3
por
trai
ts.I
f h
e ch
oose
s th
e tw
o p
hot
ogra
ph
s at
ran
dom
,fin
d t
he
pro
bab
ilit
y of
eac
h s
elec
tion
.
1.P
(2 p
ortr
ait)
�1 7�2.
P(2
lan
dsca
pe)
�2 7�3.
P(1
of
each
)�4 7�
Th
e C
aru
bas
hav
e a
coll
ecti
on o
f 28
vid
eo m
ovie
s,in
clu
din
g 12
wes
tern
s an
d
16 s
cien
ce f
icti
on.E
lise
sel
ects
3 o
f th
e m
ovie
s at
ran
dom
to
bri
ng
to a
sle
ep-o
ver
at h
er f
rien
d’s
hou
se.F
ind
th
e p
rob
abil
ity
of e
ach
sel
ecti
on.
4.P
(3 w
este
rns)
� 85 15 9�5.
P(3
sci
ence
fic
tion
)� 12 10 7�
6.P
(1 w
este
rn a
nd
2 sc
ien
ce f
icti
on)
�4 90 1�7.
P(2
wes
tern
s an
d 1
scie
nce
fic
tion
)� 28 78 3�
8.P
(3 c
omed
y)0
9.P
(2 s
cien
ce f
icti
on a
nd
2 w
este
rns)
0
For
Exe
rcis
es 1
0–13
,use
th
e ch
art
that
sh
ows
the
clas
s an
d g
end
er s
tati
stic
s fo
r th
e st
ud
ents
tak
ing
an
Alg
ebra
1 o
r A
lgeb
ra 2
cla
ss a
t L
a M
esa
Hig
h S
choo
l.If
a s
tude
nt
taki
ng
Alg
ebra
1 o
r A
lgeb
ra 2
is
sele
cted
at
ran
dom
,fin
d ea
ch p
roba
bili
ty.E
xpre
ss a
s de
cim
als
rou
nde
d to
th
e n
eare
st t
hou
san
dth
.
10.P
(sop
hom
ore/
fem
ale)
0.20
8
11.P
(ju
nio
r/m
ale)
0.14
3
12.P
(fre
shm
an/m
ale)
0.13
6
13.P
(fre
shm
an/f
emal
e)0.
145
Fin
d t
he
odd
s of
an
eve
nt
occu
rrin
g,gi
ven
th
e p
rob
abil
ity
of t
he
even
t.
14.�
5 8�5:
315
.�2 7�
2:5
16.�
3 5�3:
2
17.�
11 0�1:
918
.�5 6�
5:1
19.�
15 2�5:
7
Fin
d t
he
pro
bab
ilit
y of
an
eve
nt
occu
rrin
g,gi
ven
th
e od
ds
of t
he
even
t.
20.2
:1�2 3�
21.8
:9� 18 7�
22.4
:1�4 5�
23.1
:9� 11 0�
24.2
:7�2 9�
25.5
:9� 15 4�
Cla
ss/G
end
erN
um
ber
Fre
shm
an/M
ale
95
Fre
shm
an/F
emal
e10
1
Sop
hom
ore/
Mal
e15
4
Sop
hom
ore/
Fem
ale
145
Juni
or/M
ale
100
Juni
or/F
emal
e10
2
©G
lenc
oe/M
cGra
w-H
ill71
4G
lenc
oe A
lgeb
ra 2
A b
ag c
onta
ins
1 gr
een
,4 r
ed,a
nd
5 y
ello
w b
alls
.Tw
o b
alls
are
sel
ecte
d a
tra
nd
om.F
ind
th
e p
rob
abil
ity
of e
ach
sel
ecti
on.
1.P
(2 r
ed)
� 12 5�2.
P(1
red
an
d 1
yell
ow)
�4 9�3.
P(1
gre
en a
nd
1 ye
llow
)�1 9�
4.P
(2 g
reen
)0
5.P
(2 r
ed a
nd
1 ye
llow
)0
6.P
(1 r
ed a
nd
1 gr
een
)� 44 5�
A b
ank
con
tain
s 3
pen
nie
s,8
nic
kel
s,4
dim
es,a
nd
10
qu
arte
rs.T
wo
coin
s ar
ese
lect
ed a
t ra
nd
om.F
ind
th
e p
rob
abil
ity
of e
ach
sel
ecti
on.
7.P
(2 p
enn
ies)
� 11 00�8.
P(2
dim
es)
� 51 0�9.
P(1
nic
kel
and
1 di
me)
� 78 5�
10.P
(1 q
uar
ter
and
1 pe
nn
y)11
.P(1
qu
arte
r an
d 1
nic
kel)
12.P
(2 d
imes
an
d 1
quar
ter)
� 11 0�� 14 5�
0
Hen
rico
vis
its
a h
ome
dec
orat
ing
stor
e to
ch
oose
wal
lpap
ers
for
his
new
hou
se.T
he
stor
e h
as 2
8 b
ook
s of
wal
lpap
er s
amp
les,
incl
ud
ing
10 b
ook
s of
Wal
lPri
de
sam
ple
san
d 1
8 b
ook
s of
Del
uxe
Wal
l C
over
ings
sam
ple
s.T
he
stor
e w
ill
allo
w H
enri
co t
ob
rin
g 4
boo
ks
hom
e fo
r a
few
day
s so
he
can
dec
ide
wh
ich
wal
lpap
ers
he
wan
ts t
ob
uy.
If H
enri
co r
and
omly
ch
oose
s 4
boo
ks
to b
rin
g h
ome,
fin
d t
he
pro
bab
ilit
y of
each
sel
ecti
on.
13.P
(4 W
allP
ride
)� 12 95�
14.P
(2 W
allP
ride
an
d 2
Del
uxe
)�1 45 53 5�
15.P
(1 W
allP
ride
an
d 3
Del
uxe
)� 15 34 64 5
�16
.P(3
Wal
lPri
de a
nd
1 D
elu
xe)
� 44 58 5�
For
Exe
rcis
es 1
7–20
,use
th
e ta
ble
th
at s
how
s th
e ra
nge
of
ver
bal
SA
T s
core
s fo
rfr
esh
men
at
a sm
all
lib
eral
arts
col
lege
.If
a fr
esh
man
stu
den
t is
ch
osen
at
ran
dom
,fin
d e
ach
pro
bab
ilit
y.E
xpre
ss a
s d
ecim
als
rou
nd
ed t
o th
e n
eare
st t
hou
san
dth
.
17.P
(400
–449
)0.
052
18.P
(550
–559
)0.
243
19.P
(at
leas
t 65
0)0.
166
Fin
d t
he
odd
s of
an
eve
nt
occu
rrin
g,gi
ven
th
e p
rob
abil
ity
of t
he
even
t.
20.�
14 1�4:
721
.�1 12 3�
12:1
22.�
95 9�5:
9423
.�10
1 00�1:
999
24.�
15 6�5:
1125
.�93 5�
3:92
26.�
79 0�9:
6127
.�18 5�
8:7
Fin
d t
he
pro
bab
ilit
y of
an
eve
nt
occu
rrin
g,gi
ven
th
e od
ds
of t
he
even
t.
28.2
:23
� 22 5�29
.2:5
�2 7�30
.15:
1�1 15 6�
31.9
:7� 19 6�
32.1
1:14
�1 21 5�33
.100
0:1
�1 10 00 00 1�
34.1
2:17
�1 22 9�35
.8:1
3� 28 1�
Ran
ge
400–
449
450–
499
500–
549
550–
559
600–
649
650�
Nu
mb
er o
f S
tud
ents
129
275
438
602
620
412
Pra
ctic
e (
Ave
rag
e)
Pro
bab
ility
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-3
12-3
© Glencoe/McGraw-Hill A10 Glencoe Algebra 2
Answers (Lesson 12-3)
Readin
g t
o L
earn
Math
em
ati
csP
rob
abili
ty
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-3
12-3
©G
lenc
oe/M
cGra
w-H
ill71
5G
lenc
oe A
lgeb
ra 2
Lesson 12-3
Pre-
Act
ivit
yW
hat
do
pro
bab
ilit
y an
d o
dd
s te
ll y
ou a
bou
t li
fe’s
ris
ks?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 12
-3 a
t th
e to
p of
pag
e 64
4 in
you
r te
xtbo
ok.
Wh
at i
s th
e pr
obab
ilit
y th
at a
per
son
wil
l n
otbe
str
uck
by
ligh
tnin
g in
agi
ven
yea
r?�7 74 59 0, ,9 09 09 0
�
Rea
din
g t
he
Less
on
1.In
dica
te w
het
her
eac
h o
f th
e fo
llow
ing
stat
emen
ts i
s tr
ue
or f
alse
.
a.If
an
eve
nt
can
nev
er o
ccu
r,it
s pr
obab
ilit
y is
a n
egat
ive
nu
mbe
r.fa
lse
b.
If a
n e
ven
t is
cer
tain
to
hap
pen
,its
pro
babi
lity
is
1.tr
ue
c.If
an
eve
nt
can
su
ccee
d in
sw
ays
and
fail
in
fw
ays,
then
th
e pr
obab
ilit
y of
su
cces
s
is
.fa
lse
d.
If a
n e
ven
t ca
n s
ucc
eed
in s
way
s an
d fa
il i
n f
way
s,th
en t
he
odds
aga
inst
th
e ev
ent
are
s:f.
fals
e
e.A
pro
babi
lity
dis
trib
uti
on i
s a
fun
ctio
n i
n w
hic
h t
he
dom
ain
is
the
sam
ple
spac
e of
an
expe
rim
ent.
tru
e
2.A
wea
ther
for
ecas
t sa
ys t
hat
th
e ch
ance
of
rain
tom
orro
w i
s 40
%.
a.W
rite
th
e pr
obab
ilit
y th
at i
t w
ill
rain
tom
orro
w a
s a
frac
tion
in
low
est
term
s.�2 5�
b.
Wri
te t
he
prob
abil
ity
that
it
wil
l n
ot r
ain
tom
orro
w a
s a
frac
tion
in
low
est
term
s.�3 5�
c.W
hat
are
th
e od
ds i
n f
avor
of
rain
?2:
3
d.
Wh
at a
re t
he
odds
aga
inst
rai
n?
3:2
3.R
efer
to
the
tabl
e in
Exa
mpl
e 4
on p
age
646
in y
our
text
book
.
a.W
hat
oth
er s
um
has
th
e sa
me
prob
abil
ity
as a
su
m o
f 11
?3
b.
Wh
at a
re t
he
odds
of
roll
ing
a su
m o
f 8?
5:31
c.W
hat
are
th
e od
ds a
gain
st r
olli
ng
a su
m o
f 9?
8:1
Hel
pin
g Y
ou
Rem
emb
er
4.A
goo
d w
ay t
o re
mem
ber
som
eth
ing
is t
o ex
plai
n i
t to
som
eon
e el
se.S
upp
ose
that
you
rfr
ien
d R
ober
to i
s h
avin
g tr
oubl
e re
mem
beri
ng
the
diff
eren
ce b
etw
een
pro
babi
lity
an
dod
ds.W
hat
wou
ld y
ou t
ell
him
to
hel
p h
im r
emem
ber
this
eas
ily?
Sam
ple
an
swer
:P
rob
abili
ty g
ives
th
e ra
tio
of
succ
esse
s to
th
e to
tal
nu
mb
er o
f o
utc
om
es,w
hile
od
ds
giv
es t
he
rati
o o
f su
cces
ses
to f
ailu
res.
s � f
©G
lenc
oe/M
cGra
w-H
ill71
6G
lenc
oe A
lgeb
ra 2
Geo
met
ric
Pro
bab
ility
If a
dar
t,th
row
n a
t ra
ndo
m,h
its
the
tria
ngu
lar
boar
d sh
own
at
the
righ
t,w
hat
is
the
chan
ce t
hat
it
wil
l h
it t
he
shad
ed r
egio
n?
Th
is
chan
ce,a
lso
call
ed a
pro
babi
lity
,can
be
dete
rmin
ed b
y co
mpa
rin
g th
e ar
ea o
f th
e sh
aded
reg
ion
to
the
area
of
the
boar
d.T
his
rat
io
indi
cate
s w
hat
fra
ctio
n o
f th
e to
sses
sh
ould
hit
in
th
e sh
aded
reg
ion
.
� ��1 22 4�
or �1 2�
In g
ener
al,i
f S
is a
su
breg
ion
of
som
e re
gion
R,t
hen
th
e pr
obab
ilit
y,P
(S),
that
a p
oin
t,ch
osen
at
ran
dom
,bel
ongs
to
subr
egio
n S
is g
iven
by
the
foll
owin
g.
P(S
) �
Fin
d t
he
pro
bab
ilit
y th
at a
poi
nt,
chos
en a
t ra
nd
om,b
elon
gs t
o th
esh
aded
su
bre
gion
s of
th
e fo
llow
ing
regi
ons.
1.�1 2�
2.�5 9�
3.�� 4�
Th
e d
art
boa
rd s
how
n a
t th
e ri
ght
has
5 c
once
ntr
ic c
ircl
es
wh
ose
cen
ters
are
als
o th
e ce
nte
r of
th
e sq
uar
e b
oard
.Eac
h
sid
e of
th
e b
oard
is
38 c
m,a
nd
th
e ra
dii
of
the
circ
les
are
2 cm
,5 c
m,8
cm
,11
cm,a
nd
14
cm.A
dar
t h
itti
ng
wit
hin
on
e of
th
e ci
rcu
lar
regi
ons
scor
es t
he
nu
mb
er o
f p
oin
ts i
nd
icat
ed
on t
he
boa
rd,w
hil
e a
hit
an
ywh
ere
else
sco
res
0 p
oin
ts.I
f a
dar
t,th
row
n a
t ra
nd
om,h
its
the
boa
rd,f
ind
th
e p
rob
abil
ity
of s
cori
ng
the
ind
icat
ed n
um
ber
of
poi
nts
.
4.0
poin
ts5.
1 po
int
6.2
poin
ts
�361 3� 61
49�
�� 17 45 4� 4
�� 15 47 4� 4
�
7.3
poin
ts8.
4 po
ints
9.5
poin
ts
� 13 49 4� 4�
� 12 41 4� 4�
� 3� 61�
51
2 34
44
4 4
46
6
64
4
33
5 5
area
of
subr
egio
n S
��
�ar
e of
reg
ion
R
�1 2� (4)
(6)
� �1 2� (8)
(6)
area
of
shad
ed r
egio
n�
��
area
of
tria
ngu
lar
boar
d
44
6
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-3
12-3
© Glencoe/McGraw-Hill A11 Glencoe Algebra 2
An
swer
s
Answers (Lesson 12-4)
Stu
dy G
uid
e a
nd I
nte
rven
tion
Mu
ltip
lyin
g P
rob
abili
ties
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-4
12-4
©G
lenc
oe/M
cGra
w-H
ill71
7G
lenc
oe A
lgeb
ra 2
Lesson 12-4
Pro
bab
ility
of
Ind
epen
den
t Ev
ents
Pro
bab
ility
of T
wo
If
two
even
ts,
Aan
d B
, ar
e in
depe
nden
t, th
en t
he p
roba
bilit
y of
bot
h oc
curr
ing
isIn
dep
end
ent
Eve
nts
P(A
and
B)
�P
(A)
�P
(B).
In a
boa
rd g
ame
each
pla
yer
has
3
dif
fere
nt-
colo
red
mar
ker
s.T
o m
ove
arou
nd
th
e b
oard
th
e p
laye
r fi
rst
spin
s a
spin
ner
to
det
erm
ine
wh
ich
pie
ce c
an b
e m
oved
.He
or s
he
then
rol
ls a
die
to
det
erm
ine
how
man
y sp
aces
that
col
ored
pie
ce s
hou
ld m
ove.
On
a g
iven
tu
rn w
hat
is
the
pro
bab
ilit
y th
at a
pla
yer
wil
l b
e ab
le t
o m
ove
the
yell
ow p
iece
m
ore
than
2 s
pac
es?
Let
Abe
th
e ev
ent
that
th
e sp
inn
er l
ands
on
yel
low
,an
d le
t B
be t
he
even
t th
at t
he
die
show
s a
nu
mbe
r gr
eate
r th
an 2
.Th
e pr
obab
ilit
y of
Ais
�1 3� ,an
d th
e pr
obab
ilit
y of
Bis
�2 3� .
P(A
and
B)
�P
(A)
�P
(B)
Pro
babi
lity
of in
depe
nden
t ev
ents
��1 3�
��2 3�
or �2 9�
Sub
stitu
te a
nd m
ultip
ly.
Th
e pr
obab
ilit
y th
at t
he
play
er c
an m
ove
the
yell
ow p
iece
mor
e th
an 2
spa
ces
is �2 9� .
A d
ie i
s ro
lled
3 t
imes
.Fin
d t
he
pro
bab
ilit
y of
eac
h e
ven
t.
1.a
1 is
rol
led,
then
a 2
,th
en a
3� 21 16�
2.a
1 or
a 2
is
roll
ed,t
hen
a 3
,th
en a
5 o
r a
6� 51 4�
3.2
odd
nu
mbe
rs a
re r
olle
d,th
en a
6� 21 4�
4.a
nu
mbe
r le
ss t
han
3 i
s ro
lled
,th
en a
3,t
hen
a n
um
ber
grea
ter
than
3� 31 6�
5.A
box
con
tain
s 5
tria
ngl
es,6
cir
cles
,an
d 4
squ
ares
.If
a fi
gure
is
rem
oved
,rep
lace
d,an
da
seco
nd
figu
re i
s pi
cked
,wh
at i
s th
e pr
obab
ilit
y th
at a
tri
angl
e an
d th
en a
cir
cle
wil
l be
pic
ked?
� 12 5�o
r ab
ou
t 0.
13
6.A
bag
con
tain
s 5
red
mar
bles
an
d 4
wh
ite
mar
bles
.A m
arbl
e is
sel
ecte
d fr
om t
he
bag,
then
rep
lace
d,an
d a
seco
nd
sele
ctio
n i
s m
ade.
Wh
at i
s th
e pr
obab
ilit
y of
sel
ecti
ng
2 re
dm
arbl
es?
�2 85 1�o
r ab
ou
t 0.
31
7.A
jar
con
tain
s 7
lem
on ja
wbr
eake
rs,3
ch
erry
jaw
brea
kers
,an
d 8
rain
bow
jaw
brea
kers
.W
hat
is
the
prob
abil
ity
of s
elec
tin
g 2
lem
on ja
wbr
eake
rs i
n s
ucc
essi
on p
rovi
din
g th
eja
wbr
eake
r dr
awn
fir
st i
s th
en r
epla
ced
befo
re t
he
seco
nd
is d
raw
n?
� 34 29 4�o
r ab
ou
t0.1
5
blue
red
yello
w
Exam
ple
Exam
ple
Exer
cises
Exer
cises
©G
lenc
oe/M
cGra
w-H
ill71
8G
lenc
oe A
lgeb
ra 2
Pro
bab
ility
of
Dep
end
ent
Even
ts
Pro
bab
ility
of T
wo
If
two
even
ts,
Aan
d B
, ar
e de
pend
ent,
then
the
pro
babi
lity
of b
oth
even
ts o
ccur
ring
isD
epen
den
t E
ven
tsP
(Aan
d B
) �
P(A
) �
P(B
follo
win
g A
).
Th
ere
are
7 d
imes
an
d 9
pen
nie
s in
a w
alle
t.S
up
pos
e tw
o co
ins
are
to b
e se
lect
ed a
t ra
nd
om,w
ith
out
rep
laci
ng
the
firs
t on
e.F
ind
th
e p
rob
abil
ity
ofp
ick
ing
a p
enn
y an
d t
hen
a d
ime.
Bec
ause
th
e co
in i
s n
ot r
epla
ced,
the
even
ts a
re d
epen
den
t.
Th
us,
P(A
and
B)
�P
(A)
�P
(Bfo
llow
ing
A).
P(p
enn
y,th
en d
ime)
�P
(pen
ny)
�P
(dim
e fo
llow
ing
pen
ny)
� 19 6��
� 17 5��
�2 81 0�
Th
e pr
obab
ilit
y is
�2 81 0�or
abo
ut
0.26
Wh
at i
s th
e p
rob
abil
ity
of d
raw
ing,
wit
hou
t re
pla
cem
ent,
3 h
eart
s,th
en a
sp
ade
from
a s
tan
dar
d d
eck
of
card
s?S
ince
th
e ca
rds
are
not
rep
lace
d,th
e ev
ents
are
dep
ende
nt.
Let
H r
epre
sen
t a
hea
rt a
nd
Sre
pres
ent
a sp
ade.
P(H
,H,H
,S)
�P
(H)
�P
(H f
ollo
win
g H
) �
P(H
fol
low
ing
2 H
s) �
P(S
fol
low
ing
3 H
s)
��1 53 2�
��1 52 1�
��1 51 0�
��1 43 9�
or a
bou
t 0.
003
Th
e pr
obab
ilit
y is
abo
ut
0.00
3 of
dra
win
g 3
hea
rts,
then
a s
pade
.
Fin
d e
ach
pro
bab
ilit
y.
1.T
he
cup
on S
oph
ie’s
des
k h
olds
4 r
ed p
ens
and
7 bl
ack
pen
s.W
hat
is
the
prob
abil
ity
ofh
er s
elec
tin
g fi
rst
a bl
ack
pen
,th
en a
red
on
e?�1 54 5�
or
abo
ut
0.25
2.W
hat
is
the
prob
abil
ity
of d
raw
ing
two
card
s sh
owin
g od
d n
um
bers
fro
m a
set
of
card
sth
at s
how
th
e fi
rst
20 c
oun
tin
g n
um
bers
if
the
firs
t ca
rd i
s n
ot r
epla
ced
befo
re t
he
seco
nd
is c
hos
en?
� 39 8�o
r ab
ou
t 0.
24
3.T
her
e ar
e 3
quar
ters
,4 d
imes
,an
d 7
nic
kels
in
a c
han
ge p
urs
e.S
upp
ose
3 co
ins
are
sele
cted
wit
hou
t re
plac
emen
t.W
hat
is
the
prob
abil
ity
of s
elec
tin
g a
quar
ter,
then
a d
ime,
and
then
a n
icke
l?� 21 6�
or
abo
ut
0.04
4.A
bas
ket
con
tain
s 4
plu
ms,
6 pe
ach
es,a
nd
5 or
ange
s.W
hat
is
the
prob
abil
ity
of p
icki
ng
2 or
ange
s,th
en a
pea
ch i
f 3
piec
es o
f fr
uit
are
sel
ecte
d at
ran
dom
?� 94 1�
or
abo
ut
0.04
5.A
ph
otog
raph
er h
as t
aken
8 b
lack
an
d w
hit
e ph
otog
raph
s an
d 10
col
or p
hot
ogra
phs
for
abr
och
ure
.If
4 ph
otog
raph
s ar
e se
lect
ed a
t ra
ndo
m,w
hat
is
the
prob
abil
ity
of p
icki
ng
firs
t2
blac
k an
d w
hit
e ph
otog
raph
s,th
en 2
col
or p
hot
ogra
phs?
� 17 02�o
r ab
ou
t 0.
07
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Mu
ltip
lyin
g P
rob
abili
ties
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-4
12-4
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
© Glencoe/McGraw-Hill A12 Glencoe Algebra 2
Answers (Lesson 12-4)
Skil
ls P
ract
ice
Mu
ltip
lyin
g P
rob
abili
ties
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-4
12-4
©G
lenc
oe/M
cGra
w-H
ill71
9G
lenc
oe A
lgeb
ra 2
Lesson 12-4
A d
ie i
s ro
lled
tw
ice.
Fin
d e
ach
pro
bab
ilit
y.
1.P
(5,t
hen
6)
� 31 6�2.
P(n
o 2s
)�2 35 6�
3.P
(tw
o 1s
)� 31 6�
4.P
(an
y n
um
ber,
then
not
5)
�5 6�5.
P(4
,th
en n
ot 6
)� 35 6�
6.P
(not
1,t
hen
not
2)
�2 35 6�
A b
oard
gam
e u
ses
a se
t of
6 d
iffe
ren
t ca
rds.
Eac
h c
ard
dis
pla
ys o
ne
of t
he
foll
owin
gfi
gure
s:a
star
,a s
qu
are,
a ci
rcle
,a d
iam
ond
,a r
ecta
ngl
e,or
a p
enta
gon
.Th
e ca
rds
are
pla
ced
fac
e d
own
,an
d a
pla
yer
choo
ses
two
card
s.F
ind
eac
h p
rob
abil
ity.
7.P
(cir
cle,
then
sta
r),i
f n
o re
plac
emen
t oc
curs
� 31 0�
8.P
(dia
mon
d,th
en s
quar
e),i
f re
plac
emen
t oc
curs
� 31 6�
9.P
(2 p
olyg
ons)
,if
repl
acem
ent
occu
rs�2 35 6�
10.P
(2 p
olyg
ons)
,if
no
repl
acem
ent
occu
rs�2 3�
11.P
(cir
cle,
then
hex
agon
),if
no
repl
acem
ent
occu
rs0
Det
erm
ine
wh
eth
er t
he
even
ts a
re i
nd
epen
den
tor
dep
end
ent.
Th
en f
ind
eac
hp
rob
abil
ity.
12.A
mix
ed b
ox o
f h
erba
l te
abag
s co
nta
ins
2 le
mon
tea
bags
,3 o
ran
ge-m
ango
tea
bags
,3
cham
omil
e te
abag
s,an
d 1
apri
cot-
gin
ger
teab
ag.K
evin
ch
oose
s 2
teab
ags
at r
ando
m t
obr
ing
to w
ork
wit
h h
im.W
hat
is
the
prob
abil
ity
that
he
firs
t ch
oose
s a
lem
on t
eaba
g an
dth
en a
ch
amom
ile
teab
ag?
dep
end
ent;
� 11 2�
13.T
he
char
t sh
ows
the
sele
ctio
n o
f ol
ive
oils
th
at
Has
ha
fin
ds i
n a
spe
cial
ty f
oods
cat
alog
.If
she
ran
dom
ly s
elec
ts o
ne
type
of
oil,
then
ran
dom
lyse
lect
s an
oth
er,d
iffe
ren
t oi
l,w
hat
is
the
prob
abil
ity
that
bot
h s
elec
tion
s ar
e do
mes
tic,
firs
t co
ld p
ress
ed o
ils?
dep
end
ent;
� 82 21 0�
For
Exe
rcis
es 1
4 an
d 1
5,tw
o th
ird
s of
th
e ar
ea o
f th
e sp
inn
er
earn
s yo
u 5
0 p
oin
ts.S
up
pos
e yo
u s
pin
th
e sp
inn
er t
wic
e.
14.S
ketc
h a
tre
e di
agra
m s
how
ing
all
of t
he
poss
ibil
itie
s.U
se i
t to
fin
d th
e pr
obab
ilit
y of
spin
nin
g 50
poi
nts
,th
en 1
00 p
oin
ts.
�2 9�
15.W
hat
is
the
prob
abil
ity
that
you
get
100
poi
nts
on
eac
h s
pin
?�1 9�
50 100
50 100
2 3
50 100
2 3 2 31 3
1 31 3
100
50
Typ
e o
f O
ilD
om
esti
cIm
po
rted
Pur
e2
5
Col
d P
ress
ed4
8
Firs
t C
old
Pre
ssed
715
©G
lenc
oe/M
cGra
w-H
ill72
0G
lenc
oe A
lgeb
ra 2
A d
ie i
s ro
lled
th
ree
tim
es.F
ind
eac
h p
rob
abil
ity.
1.P
(th
ree
4s)
� 21 16�2.
P(n
o 4s
)�1 22 15 6�
3.P
(2,t
hen
3,t
hen
1)
� 21 16�4.
P(t
hre
e di
ffer
ent
even
nu
mbe
rs)
� 31 6�
5.P
(an
y n
um
ber,
then
5,t
hen
5)
� 31 6�6.
P(e
ven
nu
mbe
r,th
en o
dd n
um
ber,
then
1)
� 21 4�
Th
ere
are
3 n
ick
els,
2 d
imes
,an
d 5
qu
arte
rs i
n a
pu
rse.
Th
ree
coin
s ar
e se
lect
ed i
nsu
cces
sion
at
ran
dom
.Fin
d t
he
pro
bab
ilit
y.
7.P
(nic
kel,
then
dim
e,th
en q
uar
ter)
,if
no
repl
acem
ent
occu
rs� 21 4�
8.P
(nic
kel,
then
dim
e,th
en q
uar
ter)
,if
repl
acem
ent
occu
rs� 13 00�
9.P
(2 n
icke
ls,t
hen
1 q
uar
ter)
,if
no
repl
acem
ent
occu
rs� 21 4�
10.P
(3 d
imes
),if
rep
lace
men
t oc
curs
� 11 25�
11.P
(3 d
imes
),if
no
repl
acem
ent
occu
rs0
For
Exe
rcis
es 1
2 an
d 1
3,d
eter
min
e w
het
her
th
e ev
ents
are
in
dep
end
ent
ord
epen
den
t.T
hen
fin
d e
ach
pro
bab
ilit
y.
12.S
eren
a is
cre
atin
g a
pain
ting
.She
wan
ts t
o us
e 2
mor
e co
lors
.She
cho
oses
ran
dom
ly f
rom
6 sh
ades
of
red,
10 s
had
es o
f gr
een
,4 s
had
es o
f ye
llow
,4 s
had
es o
f pu
rple
,an
d 6
shad
esof
blu
e.W
hat
is
the
prob
abil
ity
that
sh
e ch
oose
s 2
shad
es o
f gr
een
?d
epen
den
t;� 23 9�
13.K
ersh
el’s
mot
her
is
shop
pin
g at
a b
aker
y.T
he
own
er o
ffer
s K
ersh
el a
coo
kie
from
a ja
rco
nta
inin
g 22
ch
ocol
ate
chip
coo
kies
,18
suga
r co
okie
s,an
d 15
oat
mea
l co
okie
s.W
ith
out
look
ing,
Ker
shel
sel
ects
on
e,dr
ops
it b
ack
in,a
nd
then
ran
dom
ly s
elec
ts a
not
her
.Wh
at i
sth
e pr
obab
ilit
y th
at n
eith
er s
elec
tion
was
a c
hoc
olat
e ch
ip c
ooki
e?in
dep
end
ent;
� 29 5�
14.M
ETEO
RO
LOG
YT
he
Fade
eva’
s ar
e pl
ann
ing
a 3-
day
vaca
tion
to
the
mou
nta
ins.
Alo
ng-
ran
ge f
orec
ast
repo
rts
that
th
e pr
obab
ilit
y of
rai
n e
ach
day
is
10%
.Ass
um
ing
that
the
dail
y pr
obab
ilit
ies
of r
ain
are
in
depe
nde
nt,
wh
at i
s th
e pr
obab
ilit
y th
at t
her
e is
no
rain
on
th
e fi
rst
two
days
,bu
t th
at i
t ra
ins
on t
he
thir
d da
y?� 18 01 00�
RA
ND
OM
NU
MB
ERS
For
Exe
rcis
es 1
5 an
d 1
6,u
se t
he
foll
owin
g in
form
atio
n.
An
ita
has
a l
ist
of 2
0 jo
bs a
rou
nd
the
hou
se t
o do
,an
d pl
ans
to d
o 3
of t
hem
tod
ay.S
he
assi
gns
each
job
a n
um
ber
from
1 t
o 20
,an
dse
ts h
er c
alcu
lato
r to
gen
erat
e ra
ndo
m n
um
bers
fro
m 1
to
20,w
hic
hca
n r
eocc
ur.
Of
the
jobs
,3 a
re o
uts
ide,
and
the
rest
are
in
side
.
15.S
ketc
h a
tre
e di
agra
m s
how
ing
all
of t
he
poss
ibil
itie
s th
at t
he
firs
t th
ree
nu
mbe
rs g
ener
ated
cor
resp
ond
to
insi
de jo
bs o
r ou
tsid
e jo
bs.U
se i
t to
fin
d th
e pr
obab
ilit
y th
at t
he
firs
t tw
o n
um
bers
cor
resp
ond
to i
nsi
de jo
bs,
and
the
thir
d to
an
ou
tsid
e jo
b.0.
1083
75
16.W
hat
is
the
prob
abil
ity
that
th
e n
um
ber
gen
erat
ed
corr
espo
nds
to
an o
uts
ide
job
thre
e ti
mes
in
a r
ow?
0.00
3375
I O
0.85
0.15
I O
0.85
0.15
I O
0.85
0.15
I O
0.85
0.15
I O
0.85
0.15
I O
0.85
0.15
I O
0.85
0.15
Pra
ctic
e (
Ave
rag
e)
Mu
ltip
lyin
g P
rob
abili
ties
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-4
12-4
© Glencoe/McGraw-Hill A13 Glencoe Algebra 2
An
swer
s
Answers (Lesson 12-4)
Readin
g t
o L
earn
Math
em
ati
csM
ult
iply
ing
Pro
bab
iliti
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-4
12-4
©G
lenc
oe/M
cGra
w-H
ill72
1G
lenc
oe A
lgeb
ra 2
Lesson 12-4
Pre-
Act
ivit
yH
ow d
oes
pro
bab
ilit
y ap
ply
to
bas
ket
bal
l?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 12
-4 a
t th
e to
p of
pag
e 65
1 in
you
r te
xtbo
ok.
Wri
te t
he
prob
abil
ity
that
Reg
gie
Mil
ler
mad
e a
free
-th
row
sh
ot d
uri
ng
the
1998
�99
sea
son
as
a fr
acti
on i
n l
owes
t te
rms.
(You
r an
swer
sh
ould
not
incl
ude
a d
ecim
al.)
�1 28 03 0�
Rea
din
g t
he
Less
on
1.A
bag
con
tain
s 4
yell
ow b
alls
,5 r
ed b
alls
,1 w
hit
e ba
ll,a
nd
2 bl
ack
ball
s.A
ball
is
draw
nfr
om t
he
bag
and
is n
ot r
epla
ced.
Ase
con
d ba
ll i
s dr
awn
.
a.L
et Y
be t
he
even
t “f
irst
bal
l is
yel
low
”an
d B
be t
he
even
t “s
econ
d ba
ll i
s bl
ack.
”A
reth
ese
even
ts i
nd
epen
den
tor
dep
end
ent?
dep
end
ent
b.
Tel
l w
hic
h f
orm
ula
you
wou
ld u
se t
o fi
nd
the
prob
abil
ity
that
th
e fi
rst
ball
is
yell
owan
d th
e se
con
d ba
ll i
s bl
ack.
C
A.
P(Y
and
B)
�
B.P
(Yan
d B
) �
P(Y
) �
P(B
)
C.
P(Y
and
B)
�P
(Y)
�P
(Bfo
llow
ing
Y)
c.W
hic
h e
quat
ion
sh
ows
the
corr
ect
calc
ula
tion
of
this
pro
babi
lity
?B
A.
�1 3��
� 12 1��
�1 37 3�B
.�1 3�
�� 12 1�
�� 32 3�
C.
�1 3��
�1 6��
�1 2�D
.�1 3�
��1 6�
�� 11 8�
d.
Wh
ich
equ
atio
n s
how
s th
e co
rrec
t ca
lcu
lati
on o
f th
e pr
obab
ilit
y th
at i
f th
ree
ball
s ar
edr
awn
in
su
cces
sion
wit
hou
t re
plac
emen
t,al
l th
ree
wil
l be
red
?B
A.
� 15 2��
� 15 2��
� 15 2��
� 11 72 25 8�
B.�
15 2��
� 14 1��
� 13 0��
� 21 2�
C.
� 15 2��
� 14 1��
� 13 0��
�7 61 63 0�
Hel
pin
g Y
ou
Rem
emb
er
2.S
ome
stu
den
ts h
ave
trou
ble
rem
embe
rin
g a
lot
of f
orm
ula
s,so
th
ey t
ry t
o ke
ep t
he
nu
mbe
r of
for
mu
las
they
hav
e to
kn
ow t
o a
min
imu
m.C
an y
ou l
earn
just
on
e fo
rmu
lath
at w
ill
allo
w y
ou t
o fi
nd
prob
abil
itie
s fo
r bo
th i
nde
pen
den
t an
d de
pen
den
t ev
ents
?E
xpla
in y
our
reas
onin
g.S
amp
le a
nsw
er:
Just
rem
emb
er t
he
form
ula
fo
rd
epen
den
t ev
ents
:P
(Aan
d B
) �
P(A
) �
P(B
follo
win
g A
).W
hen
th
eev
ents
are
ind
epen
den
t,P
(Bfo
llow
ing
A)
�P
(B),
so t
he
form
ula
fo
rd
epen
den
t ev
ents
sim
plif
ies
to P
(Aan
d B
) �
P(A
) �
P(B
),w
hic
h is
th
eco
rrec
t fo
rmu
la f
or
ind
epen
den
t ev
ents
.
P(Y
)�
�P
(Y)
�P
(B)
©G
lenc
oe/M
cGra
w-H
ill72
2G
lenc
oe A
lgeb
ra 2
Co
nd
itio
nal
Pro
bab
ility
Su
ppos
e a
pair
of
dice
is
thro
wn
.It
is k
now
n t
hat
th
e su
m i
s gr
eate
r th
anse
ven
.Fin
d th
e pr
obab
ilit
y th
at t
he
dice
mat
ch.
Th
e pr
obab
ilit
y of
an
eve
nt
give
n t
he
occu
rren
ce o
f an
oth
er e
ven
t is
cal
led
con
dit
ion
al p
roba
bili
ty.T
he
con
diti
onal
pro
babi
lity
of
even
t A
,th
e di
cem
atch
,giv
en e
ven
t B
,th
eir
sum
is
grea
ter
than
sev
en,i
s de
not
ed P
(A/B
).
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-4
12-4
Th
ere
are
15 s
um
s gr
eate
r th
an s
even
an
dth
ere
are
36 p
ossi
ble
pair
s al
toge
ther
.
P(B
) �
�1 35 6�
Th
ere
are
thre
e m
atch
ing
pair
s gr
eate
rth
an s
even
.
P(A
and
B)
�� 33 6�
P(A
/B)
�
P(A
/B)
�or
�1 5�
Th
e co
ndi
tion
al p
roba
bili
ty i
s �1 5� .
A c
ard
is
dra
wn
fro
m a
sta
nd
ard
dec
k o
f 52
an
d i
s fo
un
d t
o b
e re
d.
Giv
en t
hat
eve
nt,
fin
d e
ach
of
the
foll
owin
g p
rob
abil
itie
s.
1.P
(hea
rt)
�1 2�2.
P(a
ce)
� 11 3�3.
P(f
ace
card
)� 13 3�
4.P
(jac
k or
ten
)� 12 3�
5.P
(six
of
spad
es)
06.
P(s
ix o
f h
eart
s)� 21 6�
A s
por
ts s
urv
ey t
aken
at
Sti
rers
Hig
h S
choo
l sh
ows
that
48%
of
the
resp
ond
ents
lik
ed s
occe
r,66
% l
iked
bas
ket
bal
l,an
d 3
8% l
iked
hoc
key
.A
lso,
30%
lik
ed s
occe
r an
d b
ask
etb
all,
22%
lik
ed b
ask
etb
all
and
hoc
key
and
28%
lik
ed s
occe
r an
d h
ock
ey.F
inal
ly,1
2% l
iked
all
th
ree
spor
ts.
Fin
d e
ach
of
the
foll
owin
g p
rob
abil
itie
s.
7.T
he
prob
abil
ity
Meg
lik
es s
occe
r if
sh
e li
kes
bask
etba
ll.
�3 60 6�o
r � 15 1�
8.T
he
prob
abil
ity
Bif
f li
kes
bask
etba
ll i
f h
e li
kes
socc
er.
�3 40 8�o
r �5 8�
9.T
he
prob
abil
ity
Mu
ffy
like
s h
ocke
y if
sh
e li
kes
bask
etba
ll.
�2 62 6�o
r �1 3�
10.T
he
prob
abil
ity
Gre
g li
kes
hoc
key
and
bask
etba
ll i
f h
e li
kes
socc
er.
�1 42 8�o
r �1 4�
� 33 6�
� �1 35 6�P(A
and
B)
��
P(B
)
© Glencoe/McGraw-Hill A14 Glencoe Algebra 2
Answers (Lesson 12-5)
Stu
dy G
uid
e a
nd I
nte
rven
tion
Ad
din
g P
rob
abili
ties
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-5
12-5
©G
lenc
oe/M
cGra
w-H
ill72
3G
lenc
oe A
lgeb
ra 2
Lesson 12-5
Mu
tual
ly E
xclu
sive
Eve
nts
Eve
nts
th
at c
ann
ot o
ccu
r at
th
e sa
me
tim
e ar
e ca
lled
mu
tual
ly e
xclu
sive
eve
nts
.
Pro
bab
ility
of
Mu
tual
ly
If tw
o ev
ents
, A
and
B,
are
mut
ually
exc
lusi
ve,
then
Exc
lusi
ve E
ven
tsP
(Aor
B)
�P
(A)
�P
(B).
Th
is f
orm
ula
can
be
exte
nde
d to
an
y n
um
ber
of m
utu
ally
exc
lusi
ve e
ven
ts.
To
choo
se a
n a
fter
noo
n a
ctiv
ity,
sum
mer
cam
per
s p
ull
sli
ps
ofp
aper
ou
t of
a h
at.T
oday
th
ere
are
25 s
lip
s fo
r a
nat
ure
wal
k,3
5 sl
ips
for
swim
min
g,an
d 3
0 sl
ips
for
arts
an
d c
raft
s.W
hat
is
the
pro
bab
ilit
y th
at a
cam
per
wil
l p
ull
a s
lip
for
a n
atu
re w
alk
or
for
swim
min
g?T
hes
e ar
e m
utu
ally
exc
lusi
ve e
ven
ts.N
ote
that
th
ere
is a
tot
al o
f 90
sli
ps.
P(n
atu
re w
alk
or s
wim
min
g) �
P(n
atu
re w
alk)
�P
(sw
imm
ing)
��2 95 0�
��3 95 0�
or �2 3�
Th
e pr
obab
ilit
y of
a c
ampe
r’s
pull
ing
out
a sl
ip f
or a
nat
ure
wal
k or
for
sw
imm
ing
is �2 3� .
By
the
tim
e on
e te
nt
of 6
cam
per
s ge
ts t
o th
e fr
ont
of t
he
lin
e,th
ere
are
only
10
nat
ure
wal
k s
lip
s an
d 1
5 sw
imm
ing
slip
s le
ft.W
hat
is
the
pro
bab
ilit
yth
at m
ore
than
4 o
f th
e 6
cam
per
s w
ill
choo
se a
sw
imm
ing
slip
?
P(m
ore
than
4 s
wim
mer
s) �
P(5
sw
imm
ers)
�P
(6 s
wim
mer
s)
��
�0.
2T
he
prob
abil
ity
of m
ore
than
4 o
f th
e ca
mpe
rs s
wim
min
g is
abo
ut
0.2.
Fin
d e
ach
pro
bab
ilit
y.
1.A
bag
con
tain
s 45
dye
d eg
gs:1
5 ye
llow
,12
gree
n,a
nd
18 r
ed.W
hat
is
the
prob
abil
ity
ofse
lect
ing
a gr
een
or
a re
d eg
g?�2 3�
2.T
he
lett
ers
from
th
e w
ords
LO
VE
an
d L
IVE
are
pla
ced
on c
ards
an
d pu
t in
a b
ox.W
hat
is t
he
prob
abil
ity
of s
elec
tin
g an
L o
r an
O f
rom
th
e bo
x?�3 8�
3.A
pai
r of
dic
e is
rol
led,
and
the
two
nu
mbe
rs a
re a
dded
.Wh
at i
s th
e pr
obab
ilit
y th
at t
he
sum
is
eith
er a
5 o
r a
7?� 15 8�
or
abo
ut
0.28
4.A
bow
l h
as 1
0 w
hol
e w
hea
t cr
acke
rs,1
6 se
sam
e cr
acke
rs,a
nd
14 r
ye c
risp
s.If
a p
erso
npi
cks
a cr
acke
r at
ran
dom
,wh
at i
s th
e pr
obab
ilit
y of
pic
kin
g ei
ther
a s
esam
e cr
acke
r or
a ry
e cr
isp?
�3 4�
5.A
n ar
t bo
x co
ntai
ns 1
2 co
lore
d pe
ncil
s an
d 20
pas
tels
.If
5 dr
awin
g im
plem
ents
are
cho
sen
at r
ando
m,w
hat
is
the
prob
abil
ity
that
at
leas
t 4
of t
hem
are
pas
tels
?ab
ou
t 0.
37
C(1
0,0)
�C
(15,
6)�
��
C(2
5,6)
C(1
0,1)
�C
(15,
5)�
��
C(2
5,6)
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
©G
lenc
oe/M
cGra
w-H
ill72
4G
lenc
oe A
lgeb
ra 2
Incl
usi
ve E
ven
ts
Pro
bab
ility
of
Incl
usi
ve E
ven
tsIf
two
even
ts,
Aan
d B
, ar
e in
clus
ive,
P(A
or B
) �
P(A
) �
P(B
) �
P(A
and
B).
Wh
at i
s th
e p
rob
abil
ity
of d
raw
ing
a fa
ce c
ard
or
a b
lack
car
d f
rom
a st
and
ard
dec
k o
f ca
rds?
Th
e tw
o ev
ents
are
in
clu
sive
,sin
ce a
car
d ca
n b
e bo
th a
fac
e ca
rd a
nd
a bl
ack
card
.
P(f
ace
card
or
blac
k ca
rd)
�P
(fac
e ca
rd)
�P
(bla
ck c
ard)
�P
(bla
ck f
ace
card
)
�� 13 3�
��1 2�
�� 23 6�
�� 18 3�
or a
bou
t 0.
62
Th
e pr
obab
ilit
y of
dra
win
g ei
ther
a f
ace
card
or
a bl
ack
card
is
abou
t 0.
62
Fin
d e
ach
pro
bab
ilit
y.
1.W
hat
is
the
prob
abil
ity
of d
raw
ing
a re
d ca
rd o
r an
ace
fro
m a
sta
nda
rd d
eck
of c
ards
?
� 17 3�o
r ab
ou
t 0.
54
2.T
hre
e ca
rds
are
sele
cted
fro
m a
sta
nda
rd d
eck
of 5
2 ca
rds.
Wh
at i
s th
e pr
obab
ilit
y of
sele
ctin
g a
kin
g,a
quee
n,o
r a
red
card
?
�1 25 6�o
r ab
ou
t 0.
58
3.T
he
lett
ers
of t
he
alph
abet
are
pla
ced
in a
bag
.Wh
at i
s th
e pr
obab
ilit
y of
sel
ecti
ng
avo
wel
or
one
of t
he
lett
ers
from
th
e w
ord
QU
IZ?
� 27 6�o
r ab
ou
t 0.
27
4.A
pai
r of
dic
e is
rol
led.
Wh
at i
s th
e pr
obab
ilit
y th
at t
he
sum
is
odd
or a
mu
ltip
le o
f 3?
� 17 1�o
r ab
ou
t 0.
64
5.T
he
Ven
n d
iagr
am a
t th
e ri
ght
show
s th
e n
um
ber
of
ju
nio
rs o
n v
arsi
ty s
port
s te
ams
at E
lmw
ood
Hig
h S
choo
l.S
ome
ath
lete
s ar
e on
var
sity
tea
ms
for
one
seas
on o
nly
,so
me
ath
lete
s fo
r tw
o se
ason
s,an
d so
me
for
all
thre
ese
ason
s.If
a v
arsi
ty a
thle
te i
s ch
osen
at
ran
dom
fro
m
the
jun
ior
clas
s,w
hat
is
the
prob
abil
ity
that
he
or s
he
play
s a
fall
or
win
ter
spor
t?�1 13 6�
Win
ter
Jun
iors
Pla
yin
g V
arsi
ty S
po
rts
Sp
rin
g
Fall
5
6
83 5
41
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Ad
din
g P
rob
abili
ties
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-5
12-5
Exam
ple
Exam
ple
Exer
cises
Exer
cises
© Glencoe/McGraw-Hill A15 Glencoe Algebra 2
An
swer
s
Answers (Lesson 12-5)
Skil
ls P
ract
ice
Ad
din
g P
rob
abili
ties
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-5
12-5
©G
lenc
oe/M
cGra
w-H
ill72
5G
lenc
oe A
lgeb
ra 2
Lesson 12-5
Eli
has
10
bas
ebal
l ca
rds
of 1
0 d
iffe
ren
t p
laye
rs i
n h
is p
ock
et.T
hre
e p
laye
rs a
rep
itch
ers,
5 ar
e ou
tfie
lder
s,an
d 2
are
cat
cher
s.If
Eli
ran
dom
ly s
elec
ts a
car
d t
otr
ade,
fin
d e
ach
pro
bab
ilit
y.
1.P
(pit
cher
or
outf
ield
er)
�4 5�2.
P(p
itch
er o
r ca
tch
er)
�1 2�3.
P(o
utf
ield
er o
r ca
tch
er)
� 17 0�
A d
ie i
s ro
lled
.Fin
d e
ach
pro
bab
ilit
y.
4.P
(5 o
r 6)
�1 3�5.
P(a
t le
ast
a 3)
�2 3�6.
P(l
ess
than
4)
�1 2�
Det
erm
ine
wh
eth
er t
he
even
ts a
re m
utu
all
y ex
clu
sive
or i
ncl
usi
ve.T
hen
fin
d t
he
pro
bab
ilit
y.
7.A
die
is
roll
ed.W
hat
is
the
prob
abil
ity
of r
olli
ng
a 3
or a
4?
mu
tual
ly e
xclu
sive
;�1 3�
8.A
die
is
roll
ed.W
hat
is
the
prob
abil
ity
of r
olli
ng
an e
ven
nu
mbe
r or
a 4
?in
clu
sive
;�1 2�
9.A
car
d is
dra
wn
fro
m a
sta
nda
rd d
eck
of c
ards
.Wh
at i
s th
e pr
obab
ilit
y of
dra
win
g a
kin
gor
a q
uee
n?
mu
tual
ly e
xclu
sive
;� 12 3�
10.A
car
d is
dra
wn
fro
m a
sta
nda
rd d
eck
of c
ards
.Wh
at i
s th
e pr
obab
ilit
y of
dra
win
g a
jack
or a
hea
rt?
incl
usi
ve;
� 14 3�
11.T
he
soph
omor
e cl
ass
is s
elli
ng
Mot
her
’s D
ay p
lan
ts t
o ra
ise
mon
ey.S
usa
n’s
pri
ze f
orbe
ing
the
top
sell
er o
f pl
ants
is
a ch
oice
of
a bo
ok,a
CD
,or
a vi
deo.
Sh
e ca
n c
hoo
se f
rom
6 bo
oks,
3 C
Ds,
and
5 vi
deos
.Wh
at i
s th
e pr
obab
ilit
y th
at S
usa
n s
elec
ts a
boo
k or
a C
D?
mu
tual
ly e
xclu
sive
;� 19 4�
A s
pin
ner
nu
mb
ered
1�
10 i
s sp
un
.Fin
d e
ach
pro
bab
ilit
y.
12.P
(les
s th
an 5
or
even
)� 17 0�
13.P
(eve
n o
r od
d)1
14.P
(pri
me
or e
ven
)�4 5�
Tw
o ca
rds
are
dra
wn
fro
m a
sta
nd
ard
dec
k o
f ca
rds.
Fin
d e
ach
pro
bab
ilit
y.
15.P
(bot
h r
ed o
r bo
th b
lack
)�2 55 1�
16.P
(bot
h a
ces
or b
oth
red
)� 25 25 1�
17.P
(bot
h 2
s or
bot
h l
ess
than
5)
� 21 21 1�18
.P(b
oth
bla
ck o
r bo
th l
ess
than
5)
�1 68 68 3�
For
Exe
rcis
es 1
9 an
d 2
0,u
se t
he
Ven
n d
iagr
am t
hat
sh
ows
the
nu
mb
er o
f p
arti
cip
ants
in
tw
o d
iffe
ren
t k
ind
s of
aer
obic
exe
rcis
e cl
asse
s th
at a
re o
ffer
ed a
t a
hea
lth
clu
b.
Det
erm
ine
each
pro
bab
ilit
y if
a p
erso
n
is s
elec
ted
at
ran
dom
fro
m t
he
par
tici
pan
ts.
19.P
(ste
p ae
robi
cs o
r ja
zzer
cise
,bu
t n
ot b
oth
)�4 69 2�
20.P
(ste
p ae
robi
cs a
nd
jazz
erci
se)
�1 63 2�
Jazz
erci
seS
tep
Aer
ob
ics
2722
13
©G
lenc
oe/M
cGra
w-H
ill72
6G
lenc
oe A
lgeb
ra 2
An
urn
con
tain
s 7
wh
ite
mar
ble
s an
d 5
blu
e m
arb
les.
Fou
r m
arb
les
are
sele
cted
wit
hou
t re
pla
cem
ent.
Fin
d e
ach
pro
bab
ilit
y.
1.P
(4 w
hit
e or
4 b
lue)
� 98 9�2.
P(e
xact
ly 3
wh
ite)
�3 95 9�3.
P(a
t le
ast
3 w
hit
e)�1 34 3�
4.P
(few
er t
han
3 w
hit
e)�1 39 3�
5.P
(3 w
hit
e or
3 b
lue)
�4 99 9�6.
P(n
o w
hit
e or
no
blu
e)� 98 9�
Jas
on a
nd
Mar
ia a
re p
layi
ng
a b
oard
gam
e in
wh
ich
th
ree
dic
e ar
e to
ssed
to
det
erm
ine
a p
laye
r’s
mov
e.F
ind
eac
h p
rob
abil
ity.
7.P
(tw
o 5s
)� 75 2�
8.P
(th
ree
5s)
� 21 16�9.
P(a
t le
ast
two
5s)
� 22 7�
10.P
(no
5s)
�1 22 15 6�11
.P(o
ne
5)�2 75 2�
12.P
(on
e 5
or t
wo
5s)
� 15 2�
Det
erm
ine
wh
eth
er t
he
even
ts a
re m
utu
all
y ex
clu
sive
or i
ncl
usi
ve.T
hen
fin
d t
he
pro
bab
ilit
y.
13.A
cle
rk c
hoos
es 4
CD
pla
yers
at
rand
om fo
r fl
oor
disp
lays
from
a s
hipm
ent
of 2
4 C
D p
laye
rs.
If 1
5 of
the
pla
yers
hav
e a
blue
cas
e an
d th
e re
st h
ave
a re
d ca
se,w
hat
is t
he p
roba
bili
ty o
fch
oosi
ng 4
pla
yers
wit
h a
blue
cas
e or
4 p
laye
rs w
ith
a re
d ca
se?
mu
tual
.exc
lus.
;�57 01 6�
14.A
dep
artm
ent
stor
e em
ploy
s 28
hig
h s
choo
l st
ude
nts
,all
jun
iors
an
d se
nio
rs.S
ix o
f th
e12
sen
iors
are
fem
ales
an
d 12
of
the
jun
iors
are
mal
es.O
ne
stu
den
t em
ploy
ee i
s ch
osen
at r
ando
m.W
hat
is
the
prob
abil
ity
of s
elec
tin
g a
sen
ior
or a
fem
ale?
incl
usi
ve;
�4 7�
15.A
res
tau
ran
t h
as 5
pie
ces
of a
pple
pie
,4 p
iece
s of
ch
ocol
ate
crea
m p
ie,a
nd
3 pi
eces
of
blu
eber
ry p
ie.I
f Ja
nin
e se
lect
s a
piec
e of
pie
at
ran
dom
for
des
sert
,wh
at i
s th
epr
obab
ilit
y th
at s
he
sele
cts
eith
er a
pple
or
choc
olat
e cr
eam
?m
utu
ally
exc
lusi
ve;
�3 4�
16.A
t a
stat
ewid
e m
eeti
ng,t
here
are
20
scho
ol s
uper
inte
nden
ts,1
3 pr
inci
pals
,and
6 a
ssis
tant
prin
cipa
ls.I
f on
e of
th
ese
peop
le i
s ch
osen
at
ran
dom
,wh
at i
s th
e pr
obab
ilit
y th
at h
e or
she
is e
ith
er a
pri
nci
pal
or a
n a
ssis
tan
t pr
inci
pal?
mu
tual
ly e
xclu
sive
;�1 39 9�
17.A
n ai
rlin
e ha
s on
e ba
nk o
f 13
tel
epho
nes
at a
res
erva
tion
s of
fice
.Of
the
13 o
pera
tors
who
wor
k th
ere,
8 ta
ke r
eser
vati
ons
for
dom
esti
c fl
ight
s an
d 5
take
res
erva
tion
s fo
r in
tern
atio
nal
flig
hts
.Sev
en o
f th
e op
erat
ors
taki
ng
dom
esti
c re
serv
atio
ns
and
3 of
th
e op
erat
ors
taki
ng
inte
rnat
ion
al r
eser
vati
ons
are
fem
ale.
If a
n o
pera
tor
is c
hos
en a
t ra
ndo
m,w
hat
is
the
prob
abil
ity
that
th
e pe
rson
ch
osen
tak
es d
omes
tic
rese
rvat
ion
s or
is
a m
ale?
incl
usi
ve;
�1 10 3�
18.M
USI
CF
orty
sen
ior
citi
zen
s w
ere
surv
eyed
abo
ut
thei
r m
usi
c pr
efer
ence
s.T
he
resu
lts
are
disp
laye
d in
th
e V
enn
diag
ram
.If
a se
nio
r ci
tize
n f
rom
th
e su
rvey
gro
up
isse
lect
ed a
t ra
ndo
m,w
hat
is
the
prob
abil
ity
that
he
or
she
like
s on
ly c
oun
try
and
wes
tern
mu
sic?
Wh
at i
s th
epr
obab
ilit
y th
at h
e or
sh
e li
kes
clas
sica
l an
d/or
cou
ntr
y,bu
t n
ot 1
940’
s po
p?� 23 0�
;�2 5�
Co
un
try
and
Wes
tern
1940
’s P
op
Cla
ssic
al
6
9
37 6
54
Pra
ctic
e (
Ave
rag
e)
Ad
din
g P
rob
abili
ties
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-5
12-5
© Glencoe/McGraw-Hill A16 Glencoe Algebra 2
Answers (Lesson 12-5)
Readin
g t
o L
earn
Math
em
ati
csA
dd
ing
Pro
bab
iliti
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-5
12-5
©G
lenc
oe/M
cGra
w-H
ill72
7G
lenc
oe A
lgeb
ra 2
Lesson 12-5
Pre-
Act
ivit
yH
ow d
oes
pro
bab
ilit
y ap
ply
to
you
r p
erso
nal
hab
its?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 12
-5 a
t th
e to
p of
pag
e 65
8 in
you
r te
xtbo
ok.
Wh
y do
th
e pe
rcen
tage
s sh
own
on
th
e ba
r gr
aph
add
up
to m
ore
than
100%
?S
amp
le a
nsw
er:
Man
y p
eop
le d
o m
ore
th
an o
ne
of
the
liste
d b
edti
me
ritu
als.
Rea
din
g t
he
Less
on
1.In
dica
te w
het
her
th
e ev
ents
in
eac
h p
air
are
incl
usi
veor
mu
tual
ly e
xclu
sive
.
a.Q
:dra
win
g a
quee
n f
rom
a s
tan
dard
dec
k of
car
dsD
:dra
win
g a
diam
ond
from
a s
tan
dard
dec
k of
car
dsin
clu
sive
b.
J:d
raw
ing
a ja
ck f
rom
a s
tan
dard
dec
k of
car
dsK
:dra
win
g a
kin
g fr
om a
sta
nda
rd d
eck
of c
ards
mu
tual
ly e
xclu
sive
2.M
arla
too
k a
quiz
on
th
is l
esso
n t
hat
con
tain
ed t
he
foll
owin
g pr
oble
m.
Eac
h o
f th
e in
tege
rs f
rom
1 t
hro
ugh
25
is w
ritt
en o
n a
sli
p of
pap
er a
nd
plac
ed i
n a
nen
velo
pe.I
f on
e sl
ip i
s dr
awn
at
ran
dom
,wh
at i
s th
e pr
obab
ilit
y th
at i
t is
odd
or
am
ult
iple
of
5?H
ere
is M
arla
’s w
ork.
P(o
dd)
��1 23 5�
P(m
ult
iple
of
5) �
� 25 5�or
�1 5�
P(o
dd o
r m
ult
iple
of
5) �
P(o
dd)
�P
(mu
ltip
le o
f 5)
��1 23 5�
�� 25 5�
��1 28 5�
a.W
hy
is M
arla
’s w
ork
inco
rrec
t?S
amp
le a
nsw
er:
Mar
la u
sed
th
e fo
rmu
la f
or
mu
tual
ly e
xclu
sive
eve
nts
,bu
t th
e ev
ents
are
incl
usi
ve.S
he
sho
uld
use
th
e fo
rmu
la f
or
incl
usi
ve e
ven
ts s
o t
hat
th
e o
dd
mu
ltip
les
of
5 w
illn
ot
be
cou
nte
d t
wic
e.
b.
Sh
ow t
he
corr
ecte
d w
ork.
P(o
dd o
r m
ultip
le o
f 5)
�P
(odd
) �
P(m
ultip
le o
f 5)
�P
(odd
mul
tiple
of
5)
��1 23 5�
�� 25 5�
�� 23 5�
��1 25 5�
��3 5�
Hel
pin
g Y
ou
Rem
emb
er
3.S
ome
stu
den
ts h
ave
trou
ble
rem
embe
rin
g a
lot
of f
orm
ula
s,so
th
ey t
ry t
o ke
ep t
he
nu
mbe
r of
for
mu
las
they
hav
e to
kn
ow t
o a
min
imu
m.C
an y
ou l
earn
just
on
e fo
rmu
lath
at w
ill
allo
w y
ou t
o fi
nd
prob
abil
itie
s fo
r bo
th m
utu
ally
exc
lusi
ve a
nd
incl
usi
ve e
ven
ts?
Exp
lain
you
r re
ason
ing.
Sam
ple
an
swer
:Ju
st r
emem
ber
th
e fo
rmu
la f
or
incl
usi
ve e
ven
ts:
P(A
or
B)
�P
(A)
�P
(B)
�P
(Aan
d B
).W
hen
th
eev
ents
are
mu
tual
ly e
xclu
sive
,P(A
and
B)
�0,
so t
he
form
ula
fo
rin
clu
sive
eve
nts
sim
plif
ies
to P
(Aan
d B
) �
P(A
) �
P(B
),w
hic
h is
th
eco
rrec
t fo
rmu
la f
or
mu
tual
ly e
xclu
sive
eve
nts
.
©G
lenc
oe/M
cGra
w-H
ill72
8G
lenc
oe A
lgeb
ra 2
Pro
bab
ility
an
d T
ic-T
ac-T
oe
Wh
at w
ould
be
the
chan
ces
of w
inn
ing
at t
ic-t
ac-t
oe i
f it
wer
e tu
rned
in
to a
gam
e of
pu
re c
han
ce?
To
fin
d ou
t,th
e n
ine
cell
s of
th
e ti
c-ta
c-to
e bo
ard
are
nu
mbe
red
from
1 t
o 9
and
nin
e ch
ips
(als
o n
um
bere
d fr
om 1
to
9) a
re p
ut
into
a b
ag.P
laye
r A
dra
ws
a ch
ip a
t ra
ndo
m a
nd
ente
rs a
n X
in t
he
corr
espo
ndi
ng
cell
.Pla
yer
B d
oes
the
sam
e an
d en
ters
an
O.
To
solv
e th
e pr
oble
m,a
ssu
me
that
bot
h p
laye
rs d
raw
all
th
eir
chip
s w
ith
out
look
ing
and
all
Xan
d O
entr
ies
are
mad
e at
th
e sa
me
tim
e.T
her
e ar
e fo
ur
poss
ible
ou
tcom
es:a
dra
w,A
win
s,B
win
s,an
d ei
ther
A o
r B
can
win
.
Th
ere
are
16 a
rran
gem
ents
th
at r
esu
lt i
n a
dra
w.R
efle
ctio
ns
and
rota
tion
sm
ust
be
cou
nte
d as
sh
own
bel
ow.
o x
ox
o x
o o
xx
o x
4o
o x
4x
x o
8x
o x
x x
oo
x x
Th
ere
are
36 a
rran
gem
ents
in
wh
ich
eit
her
pla
yer
may
win
bec
ause
bot
hpl
ayer
s h
ave
win
nin
g tr
iple
s.
x x
xx
x x
x o
xx
x x
x x
xx
x o
o o
o4
x o
x4
x x
x4
x x
o8
o o
o8
x x
x8
x o
xo
o o
o o
oo
o o
x x
oo
o o
In t
hes
e 36
cas
es,A
’s c
han
ces
of w
inn
ing
are
�1 43 0�.
1.F
ind
the
12 a
rran
gem
ents
in
wh
ich
B w
ins
and
A c
ann
ot.
o o
xo
x o
x o
x8
x o
x4
x x
ox
x o
2.B
elow
are
12
of t
he
arra
nge
men
ts i
n w
hic
h A
win
s an
d B
can
not
.Wri
teth
e n
um
bers
to
show
th
e re
flec
tion
s an
d ro
tati
ons
for
each
arr
ange
men
t.W
hat
is
the
tota
l n
um
ber?
62
o x
ox
o x
x x
xx
x x
x o
ox
o o
x x
x1
o x
o1
x o
o4
o x
o4
x x
x4
x x
o4
o x
ox
o x
x o
oo
x o
o o
xo
o x
x x
ox
x x
x x
xx
x x
x o
ox
x o
o x
x4
o x
o8
x o
o8
x o
o8
x x
x8
o x
o8
o o
xo
o x
o x
oo
o x
o x
ox
o x
3.T
her
e ar
e � (5
9 !4! !)�
diff
eren
t an
d eq
ual
ly p
roba
ble
dist
ribu
tion
s.C
ompl
ete
the
char
t to
fin
d th
e pr
obab
ilit
y fo
r a
draw
or
for
A o
r B
to
win
.
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-5
12-5
Dra
w:
�
Aw
ins:
�
�1 43 0��
��
B w
ins:
�
�12
142
027
36
40( 126
)12 12
6
737
1260
36 � 126
62 126
8 6316 � 12
6
© Glencoe/McGraw-Hill A17 Glencoe Algebra 2
An
swer
s
Answers (Lesson 12-6)
Stu
dy G
uid
e a
nd I
nte
rven
tion
Sta
tist
ical
Mea
sure
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-6
12-6
©G
lenc
oe/M
cGra
w-H
ill72
9G
lenc
oe A
lgeb
ra 2
Lesson 12-6
Mea
sure
s o
f C
entr
al T
end
ency
Use
Wh
en
Mea
sure
s o
fm
ean
the
data
are
spr
ead
out
and
you
wan
t an
ave
rage
of
valu
es
Cen
tral
Ten
den
cym
edia
nth
e da
ta c
onta
in o
utlie
rs
mod
eth
e da
ta a
re t
ight
ly c
lust
ered
aro
und
one
or t
wo
valu
es
Fin
d t
he
mea
n,m
edia
n,a
nd
mod
e of
th
e fo
llow
ing
set
of d
ata:
{42,
39,3
5,40
,38,
35,4
5}.
To
fin
d th
e m
ean
,add
th
e va
lues
an
d di
vide
by
the
nu
mbe
r of
val
ues
.
mea
n �
�39
.14.
To
fin
d th
e m
edia
n,a
rran
ge t
he
valu
es i
n a
scen
din
g or
des
cen
din
g or
der
and
choo
se t
he
mid
dle
valu
e.(I
f th
ere
is a
n e
ven
nu
mbe
r of
val
ues
,fin
d th
e m
ean
of
the
two
mid
dle
valu
es.)
In t
his
cas
e,th
e m
edia
n i
s 39
.T
o fi
nd
the
mod
e,ta
ke t
he
mos
t co
mm
on v
alu
e.In
th
is c
ase,
the
mod
e is
35.
Fin
d t
he
mea
n,m
edia
n,a
nd
mod
e of
eac
h s
et o
f d
ata.
Rou
nd
to
the
nea
rest
hu
nd
red
th,i
f n
eces
sary
.
1.{2
38,2
61,2
45,2
49,2
55,2
62,2
41,2
45}
249.
5;24
7;24
5
2.{9
,13,
8,10
,11,
9,12
,16,
10,9
}10
.7;
10;
9
3.{1
20,1
08,1
45,1
29,1
02,1
32,1
34,1
18,1
08,1
42}
123.
8;12
4.5;
108
4.{6
8,54
,73,
58,6
3,72
,65,
70,6
1}64
.89;
65;
no
mo
de
5.{3
4,49
,42,
38,4
0,45
,34,
28,4
3,30
}38
.3;
39;
34
6.T
he
tabl
e at
th
e ri
ght
show
s th
e po
pula
tion
s of
th
e
six
New
En
glan
d ca
pita
ls.W
hic
h w
ould
be
the
mos
t ap
prop
riat
e m
easu
re o
f ce
ntr
al t
ende
ncy
to
repr
esen
t th
e da
ta?
Exp
lain
wh
y an
d fi
nd
that
val
ue.
Sour
ce: w
ww.fa
ctfin
der.c
ensu
s.gov
Th
ere
is n
o m
od
e.T
he
po
pu
lati
on
of
Bo
sto
n is
an
ou
tlie
r an
d
wo
uld
rai
se t
he
mea
n t
oo
hig
h.T
he
med
ian
,79
,500
,wo
uld
be
the
bes
t ch
oic
e.
Cit
yP
op
ula
tio
n (
rou
nd
edto
th
e n
eare
st 1
000)
Aug
usta
, M
E19
,000
Bos
ton,
MA
589,
000
Con
cord
, N
H37
,000
Har
tford
, C
T12
2,00
0
Mon
tpel
ier,
VT
8,00
0
Pro
vide
nce,
RI
174,
000
42 �
39 �
35 �
40 �
38 �
35 �
45�
��
��
7
Exam
ple
Exam
ple
Exer
cises
Exer
cises
©G
lenc
oe/M
cGra
w-H
ill73
0G
lenc
oe A
lgeb
ra 2
Mea
sure
s o
f V
aria
tio
nT
he
ran
gean
d th
e st
and
ard
dev
iati
onm
easu
re h
owsc
atte
red
a se
t of
dat
a is
.
Sta
nd
ard
If a
set
of d
ata
cons
ists
of
the
nva
lues
x1,
x2,
…,
x nan
d ha
s m
ean
x �, t
hen
the
stan
dard
dev
iatio
n
Dev
iati
on
is g
iven
by
��
���
.
Th
e sq
uar
e of
th
e st
anda
rd d
evia
tion
is
call
ed t
he
vari
ance
.
Fin
d t
he
vari
ance
an
d s
tan
dar
d d
evia
tion
of
the
dat
a se
t {1
0,9,
6,9,
18,4
,8,2
0}.
Ste
p 1
Fin
d th
e m
ean
.
x ��
�10
.5
Ste
p 2
Fin
d th
e va
rian
ce.
�2
�S
tand
ard
varia
nce
form
ula
� �or
27.
5
Ste
p 3
Fin
d th
e st
anda
rd d
evia
tion
.�
��
27.5
��
5.2
Th
e va
rian
ce i
s 27
.5 a
nd
the
stan
dard
dev
iati
on i
s ab
out
5.2.
Fin
d t
he
vari
ance
an
d s
tan
dar
d d
evia
tion
of
each
set
of
dat
a.R
oun
d t
o th
en
eare
st t
enth
.
1.{1
00,8
9,11
2,10
4,96
,108
,93}
2.{6
2,54
,49,
62,4
8,53
,50}
58.5
;7.
629
.4;
5.4
3.{8
,9,8
,8,9
,7,8
,9,6
}4.
{4.2
,5.0
,4.7
,4.5
,5.2
,4.8
,4.6
,5.1
}0.
9;0.
90.
1;0.
3
5.T
he
tabl
e at
th
e ri
ght
list
s th
e pr
ices
of
ten
bra
nds
of
brea
kfas
t ce
real
.Wh
at i
s th
e st
anda
rd d
evia
tion
of
the
valu
es t
o th
e n
eare
st p
enn
y?$0
.33
Pri
ce o
f 10
Bra
nd
so
f B
reak
fast
Cer
eal
$2.2
9$3
.19
$3.3
9$2
.79
$2.9
9$3
.09
$3.1
9$2
.59
$2.7
9$3
.29
220
�8(10
�10
.5)2
�(9
�10
.5)2
�…
�(2
0 �
10.5
)2�
��
��
�8
(x1
�x �)
2�
(x2
�x �)
2�
… �
(xn
�x �)
2�
��
��
n
10 �
9 �
6 �
9 �
18 �
4 �
8 �
20�
��
��
8
(x1
�x �)
2�
(x2
�x �)
2�
… �
(xn
�x �)
2
��
��
�n
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Sta
tist
ical
Mea
sure
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-6
12-6
Exam
ple
Exam
ple
Exer
cises
Exer
cises
© Glencoe/McGraw-Hill A18 Glencoe Algebra 2
Answers (Lesson 12-6)
Skil
ls P
ract
ice
Sta
tist
ical
Mea
sure
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-6
12-6
©G
lenc
oe/M
cGra
w-H
ill73
1G
lenc
oe A
lgeb
ra 2
Lesson 12-6
Fin
d t
he
vari
ance
an
d s
tan
dar
d d
evia
tion
of
each
set
of
dat
a to
th
e n
eare
st t
enth
.
1.{3
2,41
,35,
35,4
6,42
}23
.6,4
.9
2.{1
3,62
,77,
24,3
8,19
,88}
763.
8,27
.6
3.{8
9,99
,42,
16,4
2,71
,16}
959.
1,31
.0
4.{4
50,4
00,6
25,2
25,3
00,7
50,6
50,6
25}
30,5
37.1
;17
4.7
5.{1
7,23
,65,
94,3
3,33
,33,
8,57
,75,
44,1
2,11
,68,
39}
630.
7,25
.1
6.{7
.2,3
.1,3
.8,9
.5,8
.3,8
.4}
5.8,
2.4
7.{1
.5,2
.5,3
.5,4
.5,4
.5,5
.5,6
.5,7
.5}
3.5,
1.9
For
Exe
rcis
es 8
an
d 9
,use
th
e ta
ble
th
at s
how
s th
e p
rofi
t in
bil
lion
s of
dol
lars
rep
orte
d b
y U
.S.m
anu
fact
ure
rs f
or t
he
firs
t q
uar
ter
of t
he
year
s fr
om 1
997
thro
ugh
200
1.
Sour
ce: U
. S. C
ensu
s Bur
eau
8.F
ind
the
mea
n an
d m
edia
n of
the
dat
a to
the
nea
rest
ten
th.
$64.
3 b
illio
n,$
61.4
bill
ion
9.W
hic
h m
easu
re o
f ce
ntr
al t
ende
ncy
bes
t re
pres
ents
th
e da
ta?
Exp
lain
.T
he
med
ian
is m
ore
rep
rese
nta
tive
bec
ause
th
e va
lue
45.3
is n
ot
clo
se t
oth
e o
ther
dat
a p
oin
ts,a
nd
it lo
wer
s th
e m
ean
.
For
Exe
rcis
es 1
0 an
d 1
1,u
se t
he
tab
le t
hat
sh
ows
the
per
cen
t of
fou
rth
gra
de
stu
den
ts r
ead
ing
at o
r ab
ove
the
pro
fici
ency
lev
el i
n a
nat
ion
ally
-ad
min
iste
red
read
ing
asse
ssm
ent.
Sour
ce: N
atio
nal C
ente
r for
Edu
catio
n St
atist
ics
10.F
ind
the
mea
n,m
edia
n,a
nd
stan
dard
dev
iati
on o
f th
e da
ta t
o th
e n
eare
st t
enth
.30
.5%
,30.
5%,1
.1
11.W
hat
do
the
stat
isti
cs f
rom
Exe
rcis
e 11
tel
l yo
u a
bou
t th
e da
ta?
Sam
ple
an
swer
:S
ince
th
e m
edia
n a
nd
mea
n a
re e
qu
al a
nd
th
e st
and
ard
dev
iati
on
is s
mal
l,th
e p
erce
nt
of
stu
den
ts r
ead
ing
at
or
abov
e th
ep
rofi
cien
cy le
vel h
as n
ot
vari
ed m
uch
fro
m 1
992
to 2
000.
Year
1992
1994
1998
2000
Per
cen
t at
or
abov
e p
rofi
cien
cy le
vel
29%
30%
31%
32%
Year
1997
1998
1999
2000
2001
Sea
son
ally
-Ad
just
ed
Pro
fit
($ b
illio
ns)
$61.
4$7
5.6
$60.
9$7
8.5
$45.
3
©G
lenc
oe/M
cGra
w-H
ill73
2G
lenc
oe A
lgeb
ra 2
Fin
d t
he
vari
ance
an
d s
tan
dar
d d
evia
tion
of
each
set
of
dat
a to
th
e n
eare
st t
enth
.
1.{4
7,61
,93,
22,8
2,22
,37}
2.{1
0,10
,54,
39,9
6,91
,91,
18}
673.
1,25
.912
28.6
,35.
1
3.{1
,2,2
,3,3
,3,4
,4,4
,4,5
,5,5
,5,5
}4.
{110
0,72
5,85
0,33
5,70
0,80
0,95
0}1.
6,1.
249
,150
.0;
221.
7
5.{3
.4,7
.1,8
.5,5
.1,4
.7,6
.3,9
.9,8
.4,3
.6}
6.{2
.8,0
.5,1
.9,0
.8,1
.9,1
.5,3
.3,2
.6,0
.7,2
.5}
4.7,
2.2
0.8,
0.9
7.H
EALT
H C
AR
EE
igh
t ph
ysic
ian
s w
ith
15
pati
ents
on
a h
ospi
tal
floo
r se
e th
ese
pati
ents
an a
vera
ge o
f 18
min
ute
s a
day.
Th
e 22
nu
rses
on
th
e sa
me
floo
r se
e th
e pa
tien
ts a
nav
erag
e of
3 h
ours
a d
ay.A
s a
hos
pita
l ad
min
istr
ator
,wou
ld y
ou q
uot
e th
e m
ean
,m
edia
n,o
r m
ode
as a
n i
ndi
cato
r of
th
e am
oun
t of
dai
ly m
edic
al a
tten
tion
th
e pa
tien
ts o
nth
is f
loor
rec
eive
? E
xpla
in.
Eit
her
th
e m
edia
n o
r th
e m
od
e;th
ey a
re e
qu
al a
nd
hig
her
th
an t
he
mea
n,w
hic
h is
low
ered
by
the
smal
ler
amo
un
t o
f ti
me
the
phy
sici
ans
spen
d w
ith
th
e p
atie
nts
.
For
Exe
rcis
es 8
–10,
use
th
e fr
equ
ency
tab
le t
hat
sh
ows
the
per
cen
t of
pu
bli
c sc
hoo
lte
ach
ers
in t
he
U.S
.in
199
9 w
ho
use
d c
omp
ute
rs o
r th
eIn
tern
et a
t sc
hoo
l fo
r va
riou
sad
min
istr
ativ
e an
d t
each
ing
acti
viti
es.
8.F
ind
the
mea
n,m
edia
n,an
d m
ode
of t
he
data
.17
.75%
,12%
,8%
9.S
uppo
se y
ou b
elie
ve t
each
ers
use
com
pute
rs o
r th
e In
tern
et t
ooin
freq
uen
tly.
Wh
ich
mea
sure
w
ould
you
quo
te a
s th
e “a
vera
ge?”
Sour
ce: N
atio
nal A
sses
smen
t of E
duca
tiona
l Pro
gres
s
Exp
lain
.M
od
e;it
is lo
wes
t.
10.S
upp
ose
you
bel
ieve
tea
cher
s u
se c
ompu
ters
or
the
Inte
rnet
too
oft
en.W
hic
h m
easu
rew
ould
you
qu
ote
as t
he
“ave
rage
?”E
xpla
in.
Mea
n;
it is
hig
hes
t.
For
Exe
rcis
es 1
1 an
d 1
2,u
se t
he
freq
uen
cy t
able
th
at
show
s th
e n
um
ber
of
gam
es p
laye
d b
y 24
Am
eric
an
Lea
gue
bas
ebal
l p
laye
rs b
etw
een
op
enin
g d
ay,2
001
and
Sep
tem
ber
8,2
001.
11.F
ind
the
mea
n,m
edia
n,m
ode,
and
stan
dard
dev
iati
on o
f th
en
um
ber
of g
ames
pla
yed
to t
he
nea
rest
ten
th.
138.
2,13
8;13
8,2.
0
12.F
or h
ow m
any
play
ers
is t
he
nu
mbe
r of
gam
es w
ith
in o
ne
stan
dard
dev
iati
on o
f th
e m
ean
?14
Sour
ce: M
ajor L
eagu
e Ba
seba
ll
No
.of
Gam
esF
req
uen
cy
141
4
140
3
139
4
138
5
137
2
136
3
135
3
Per
cen
t U
sin
g
Act
ivit
yC
om
pu
ter
or
Inte
rnet
Cre
ate
inst
ruct
iona
l mat
eria
ls39
Adm
inis
trat
ive
reco
rd k
eepi
ng34
Com
mun
icat
e w
ith c
olle
ague
s23
Gat
her
info
rmat
ion
for
plan
ning
less
ons
16
Mul
timed
ia c
lass
room
pre
sent
atio
ns8
Acc
ess
rese
arch
and
bes
t pr
actic
es f
or t
each
ing
8
Com
mun
icat
e w
ith p
aren
ts o
r st
uden
ts8
Acc
ess
mod
el le
sson
pla
ns6
Pra
ctic
e (
Ave
rag
e)
Sta
tist
ical
Mea
sure
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-6
12-6
© Glencoe/McGraw-Hill A19 Glencoe Algebra 2
An
swer
s
Answers (Lesson 12-6)
Readin
g t
o L
earn
Math
em
ati
csS
tati
stic
al M
easu
res
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-6
12-6
©G
lenc
oe/M
cGra
w-H
ill73
3G
lenc
oe A
lgeb
ra 2
Lesson 12-6
Pre-
Act
ivit
yW
hat
sta
tist
ics
shou
ld a
tea
cher
tel
l th
e cl
ass
afte
r a
test
?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 12
-6 a
t th
e to
p of
pag
e 66
4 in
you
r te
xtbo
ok.
Th
ere
is m
ore
than
on
e w
ay t
o gi
ve a
n “
aver
age”
scor
e fo
r th
is t
est.
Th
ree
mea
sure
s of
cen
tral
ten
denc
y fo
r th
ese
scor
es a
re 9
4,76
.5 a
nd 7
3.9.
Can
you
tell
whi
ch o
f th
ese
is t
he m
ean,
the
med
ian,
and
the
mod
e w
itho
ut d
oing
any
calc
ula
tion
s? E
xpla
in y
our
answ
er.
Sam
ple
an
swer
:Yes
.Th
e m
od
e m
ust
be
on
e o
f th
e sc
ore
s,so
itm
ust
be
an in
teg
er.T
he
med
ian
mu
st b
e ei
ther
on
e o
f th
esc
ore
s o
r h
alfw
ay b
etw
een
tw
o o
f th
e sc
ore
s,so
it m
ust
be
anin
teg
er o
r a
dec
imal
en
din
g w
ith
.5.T
her
efo
re,9
4 is
th
e m
od
e,76
.5 is
th
e m
edia
n,a
nd
73.
9 is
th
e m
ean
.
Rea
din
g t
he
Less
on
1.M
atch
eac
h m
easu
re w
ith
on
e of
th
e si
x de
scri
ptio
ns
of h
ow t
o fi
nd
mea
sure
s of
cen
tral
ten
den
cy a
nd
vari
atio
n.
a.m
edia
nvi
b.m
ode
ic.
ran
geiv
d.
vari
ance
iiie.
mea
nii
f.st
anda
rd d
evia
tion
v
i.F
ind
the
mos
t co
mm
only
occ
urr
ing
valu
es o
r va
lues
in
a s
et o
f da
ta.
ii.A
dd t
he
data
an
d di
vide
by
the
nu
mbe
r of
ite
ms.
iii.
Fin
d th
e m
ean
of
the
squ
ares
of
the
diff
eren
ces
betw
een
eac
h v
alu
e in
th
e se
t of
dat
aan
d th
e m
ean
.
iv.
Fin
d th
e di
ffer
ence
bet
wee
n t
he
larg
est
and
smal
lest
val
ues
in
th
e se
t of
dat
a.
v.T
ake
the
posi
tive
squ
are
root
of
the
vari
ance
.
vi.I
f th
ere
is a
n o
dd n
um
ber
of i
tem
s in
a s
et o
f da
ta,t
ake
the
mid
dle
one.
If t
her
e is
an
even
nu
mbe
r of
ite
ms,
add
the
two
mid
dle
item
s an
d di
vide
by
2.
Hel
pin
g Y
ou
Rem
emb
er
2.It
is
usu
ally
eas
ier
to r
emem
ber
a co
mpl
icat
ed p
roce
dure
if
you
bre
ak i
t do
wn
in
to s
teps
.W
rite
th
e pr
oced
ure
for
fin
din
g th
e st
anda
rd d
evia
tion
for
a s
et o
f da
ta i
n a
ser
ies
ofbr
ief,
nu
mbe
red
step
s.
Sam
ple
an
swer
:1.
Fin
d t
he
mea
n.
2.F
ind
th
e d
iffe
ren
ce b
etw
een
eac
h v
alu
e an
d t
he
mea
n.
3.S
qu
are
each
dif
fere
nce
.4.
Fin
d t
he
mea
n o
f th
e sq
uar
es.
5.Ta
ke t
he
po
siti
ve s
qu
are
roo
t.
©G
lenc
oe/M
cGra
w-H
ill73
4G
lenc
oe A
lgeb
ra 2
Pro
bab
iliti
es in
Gen
etic
sG
enes
are
the
un
its
wh
ich
tra
nsm
it h
ered
itar
y tr
aits
.Th
e po
ssib
le f
orm
sw
hic
h a
gen
e m
ay t
ake,
dom
inan
tan
d re
cess
ive,
are
call
ed a
llel
es.A
part
icu
lar
trai
t is
det
erm
ined
by
two
alle
les,
one
from
th
e fe
mal
e pa
ren
t an
don
e fr
om t
he
mal
e pa
ren
t.If
an
org
anis
m h
as t
he
trai
t w
hic
h i
s do
min
ant,
itm
ay h
ave
eith
er t
wo
dom
inan
t al
lele
s or
on
e do
min
ant
and
one
rece
ssiv
eal
lele
.If
the
orga
nis
m h
as t
he
trai
t w
hic
h i
s re
cess
ive,
it m
ust
hav
e tw
ore
cess
ive
alle
les.
Con
sid
er a
pla
nt
in w
hic
h t
all
stem
s,T
,are
dom
inan
t to
shor
t st
ems,
t.W
hat
is
the
pro
bab
ilit
y of
ob
tain
ing
a lo
ng-
stem
med
pla
nt
if t
wo
lon
g-st
emm
ed p
lan
ts b
oth
wit
h t
he
gen
etic
for
mu
la T
tar
e cr
osse
d?
A P
un
net
t sq
uar
eis
a c
har
t u
sed
to d
eter
min
e th
e po
ssib
le
com
bin
atio
ns
of c
har
acte
rist
ics
amon
g of
fspr
ing.
3 ta
ll-s
tem
med
�1
shor
t-st
emm
ed4
tota
l
Th
us,
the
prob
abil
ity
is �3 4� .
In a
cer
tain
pla
nt,
red
flo
wer
s,R
,are
dom
inan
t to
wh
ite
flow
ers,
r.If
a w
hit
e-fl
ower
ed p
lan
t,rr
is c
ross
ed w
ith
a r
ed-f
low
ered
pla
nt,
Rr,
fin
d t
he
pro
bab
ilit
y of
eac
h o
f th
e fo
llow
ing.
1.w
hit
e-fl
ower
ed p
lan
t�1 2�
2.re
d-fl
ower
ed p
lan
t�1 2�
In a
cer
tain
pla
nt,
tall
,T,i
s d
omin
ant
to s
hor
t,t,
and
gre
en p
ods,
G,
are
dom
inan
t to
yel
low
pod
s,g.
Pla
nts
wit
h t
he
gen
etic
for
mu
las
TtG
gan
d T
TG
gar
e cr
osse
d.F
ind
th
e p
rob
abil
ity
of e
ach
of
the
foll
owin
g.
3.ta
ll p
lan
t w
ith
gre
en p
ods
�3 4�4.
tall
pla
nt
wit
h y
ello
w p
ods
�1 4�
TT
Tt
Tt
Tt
T tttEn
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-6
12-6
Exam
ple
Exam
ple
© Glencoe/McGraw-Hill A20 Glencoe Algebra 2
Answers (Lesson 12-7)
Stu
dy G
uid
e a
nd I
nte
rven
tion
Th
e N
orm
al D
istr
ibu
tio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-7
12-7
©G
lenc
oe/M
cGra
w-H
ill73
5G
lenc
oe A
lgeb
ra 2
Lesson 12-7
No
rmal
an
d S
kew
ed D
istr
ibu
tio
ns
A c
onti
nu
ous
pro
bab
ilit
ydi
stri
buti
on i
sre
pres
ente
d by
a c
urv
e.
Typ
es o
f
No
rmal
Po
siti
vely
Ske
wed
Neg
ativ
ely
Ske
wed
Co
nti
nu
ou
sD
istr
ibu
tio
ns
Det
erm
ine
wh
eth
er t
he
dat
a b
elow
ap
pea
r to
be
pos
itiv
ely
skew
ed,
neg
ati
vely
sk
ewed
,or
nor
ma
lly
dis
trib
ute
d.
{100
,120
,110
,100
,110
,80,
100,
90,1
00,1
20,1
00,9
0,11
0,10
0,90
,80,
100,
90}
Mak
e a
freq
uen
cy t
able
for
th
e da
ta.
Th
en u
se t
he
data
to
mak
e a
his
togr
am.
Sin
ce t
he
his
togr
am i
s ro
ugh
ly s
ymm
etri
c,th
e da
ta a
ppea
r to
be
nor
mal
ly d
istr
ibu
ted.
Det
erm
ine
wh
eth
er t
he
dat
a in
eac
h t
able
ap
pea
r to
be
pos
itiv
ely
skew
ed,
neg
ati
vely
sk
ewed
,or
nor
ma
lly
dis
trib
ute
d.M
ake
a h
isto
gram
of
the
dat
a.
1.{2
7,24
,29,
25,2
7,22
,24,
25,2
9,24
,25,
22,2
7,24
,22,
25,2
4,22
}p
osi
tive
ly s
kew
ed
2.
no
rmal
ly d
istr
ibu
ted
3.n
egat
ivel
y sk
ewed
�10
010
1–12
012
1–14
014
1–16
016
1–18
018
1–20
020
0�
12 10 8 6 4 2Frequency
Tho
usa
nd
s o
f D
olla
rs
Ho
usi
ng
Pri
ceN
o.o
f H
ou
ses
So
ld
less
tha
n $1
00,0
000
$100
,00�
$120
,000
1
$121
,00�
$140
,000
3
$141
,00�
$160
,000
7
$161
,00�
$180
,000
8
$181
,00�
$200
,000
6
over
$20
0,00
012
104
8 6 4 2Frequency
56
78
9
Sh
oe
Siz
e4
56
78
910
No
.of
Stu
den
ts1
24
85
12
22
6 4 2 Frequency
2425
2729
Val
ue
8090
100
110
120
Fre
qu
ency
24
73
2
80
6 4 2
Frequency
9010
011
012
0
Exam
ple
Exam
ple
Exer
cises
Exer
cises
©G
lenc
oe/M
cGra
w-H
ill73
6G
lenc
oe A
lgeb
ra 2
Use
No
rmal
Dis
trib
uti
on
s
No
rmal
Dis
trib
uti
on
Nor
mal
dis
trib
utio
ns h
ave
thes
e pr
oper
ties.
The
gra
ph is
max
imiz
ed a
t th
e m
ean.
The
mea
n, m
edia
n, a
nd m
ode
are
abou
t eq
ual.
Abo
ut 6
8% o
f th
e va
lues
are
with
in o
ne s
tand
ard
devi
atio
n of
the
mea
n.A
bout
95%
of
the
valu
es a
re w
ithin
tw
o st
anda
rd d
evia
tions
of
the
mea
n.A
bout
99%
of
the
valu
es a
re w
ithin
thr
ee s
tand
ard
devi
atio
ns o
f th
e m
ean.
Th
e h
eigh
ts o
f p
laye
rs i
n a
bas
ket
bal
l le
agu
e ar
e n
orm
ally
dis
trib
ute
d w
ith
a m
ean
of
6 fe
et 1
in
ch a
nd
a s
tan
dar
d d
evia
tion
of
2 in
ches
.
a.W
hat
is
the
pro
bab
ilit
y th
at a
pla
yer
sele
cted
at
ran
dom
wil
l b
e sh
orte
r th
an 5
fee
t 9
inch
es?
Dra
w a
nor
mal
cu
rve.
Lab
el t
he
mea
n a
nd
the
mea
n p
lus
or m
inu
s m
ult
iple
s of
th
e st
anda
rd d
evia
tion
.T
he
valu
e of
5 f
eet
9 in
ches
is
2 st
anda
rd d
evia
tion
s be
low
th
e m
ean
,so
appr
oxim
atel
y 2.
5% o
f th
e pl
ayer
s w
ill
be s
hor
ter
than
5 f
eet
9 in
ches
.
b.
If t
her
e ar
e 24
0 p
laye
rs i
n t
he
leag
ue,
abou
t h
ow m
any
pla
yers
are
tal
ler
than
6fe
et 3
in
ches
?T
he
valu
e of
6 f
eet
3 in
ches
is
one
stan
dard
dev
iati
on a
bove
th
e m
ean
.App
roxi
mat
ely
16%
of
the
play
ers
wil
l be
tal
ler
than
th
is h
eigh
t.24
0 �
0.16
�38
Abo
ut
38 o
f th
e pl
ayer
s ar
e ta
ller
th
an 6
fee
t 3
inch
es.
EGG
PR
OD
UC
TIO
NT
he
nu
mb
er o
f eg
gs l
aid
per
yea
r b
y a
par
ticu
lar
bre
ed o
fch
ick
en i
s n
orm
ally
dis
trib
ute
d w
ith
a m
ean
of
225
and
a s
tan
dar
d d
evia
tion
of
10 e
ggs.
1.A
bou
t w
hat
per
cen
t of
th
e ch
icke
ns
wil
l la
y be
twee
n 2
15 a
nd
235
eggs
per
yea
r? 6
8%
2.In
a f
lock
of
400
chic
ken
s,ab
out
how
man
y w
ould
you
exp
ect
to l
ay m
ore
than
245
egg
spe
r ye
ar?
10 c
hic
ken
s
MA
NU
FAC
TUR
ING
Th
e d
iam
eter
of
bol
ts p
rod
uce
d b
y a
man
ufa
ctu
rin
g p
lan
t is
nor
mal
ly d
istr
ibu
ted
wit
h a
mea
n o
f 18
mm
an
d a
sta
nd
ard
dev
iati
on o
f 0.
2 m
m.
3.W
hat
per
cen
t of
bol
ts c
omin
g of
f of
th
e as
sem
bly
lin
e h
ave
a di
amet
er g
reat
er t
han
18
.4 m
m?
2.5%
4.W
hat
per
cen
t h
ave
a di
amet
er b
etw
een
17.
8 an
d 18
.2 m
m?
68%
5'7"
5'9"
5'11
"6'
1"6'
3"6'
5"6'
7"
�3
mea
n
�2
�
�
�2
�3
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Th
e N
orm
al D
istr
ibu
tio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-7
12-7
Exam
ple
Exam
ple
Exer
cises
Exer
cises
© Glencoe/McGraw-Hill A21 Glencoe Algebra 2
An
swer
s
Answers (Lesson 12-7)
Skil
ls P
ract
ice
Th
e N
orm
al D
istr
ibu
tio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-7
12-7
©G
lenc
oe/M
cGra
w-H
ill73
7G
lenc
oe A
lgeb
ra 2
Lesson 12-7
Det
erm
ine
wh
eth
er t
he
dat
a in
eac
h t
able
ap
pea
r to
be
pos
itiv
ely
skew
ed,
neg
ati
vely
sk
ewed
,or
nor
ma
lly
dis
trib
ute
d.
1.2.
no
rmal
ly d
istr
ibu
ted
neg
ativ
ely
skew
ed
For
Exe
rcis
es 3
an
d 4
,use
th
e fr
equ
ency
tab
le t
hat
sh
ows
the
aver
age
nu
mb
er o
f d
ays
pat
ien
ts s
pen
t on
th
esu
rgic
al w
ard
of
a h
osp
ital
las
t ye
ar.
3.M
ake
a h
isto
gram
of
the
data
.
4.D
o th
e da
ta a
ppea
r to
be
posi
tive
lysk
ewed
,neg
ativ
ely
skew
ed,o
r n
orm
ally
dis
trib
ute
d?
Exp
lain
.P
osi
tive
ly s
kew
ed;
the
his
tog
ram
is h
igh
at
the
left
an
d h
as a
tai
l to
th
e ri
gh
t.
DEL
IVER
YF
or E
xerc
ises
5–7
,use
th
e fo
llow
ing
info
rmat
ion
.T
he
tim
e it
tak
es a
bic
ycle
cou
rier
to
deli
ver
a pa
rcel
to
his
far
thes
t cu
stom
er i
s n
orm
ally
dist
ribu
ted
wit
h a
mea
n o
f 40
min
ute
s an
d a
stan
dard
dev
iati
on o
f 4
min
ute
s.
5.A
bout
wha
t pe
rcen
t of
the
cou
rier
’s t
rips
to
this
cus
tom
er t
ake
betw
een
36 a
nd 4
4 m
inut
es?
68%
6.A
bout
wha
t pe
rcen
t of
the
cou
rier
’s t
rips
to
this
cus
tom
er t
ake
betw
een
40 a
nd 4
8 m
inut
es?
47.5
%7.
Abo
ut w
hat
perc
ent
of t
he c
ouri
er’s
tri
ps t
o th
is c
usto
mer
tak
e le
ss t
han
32 m
inut
es?
2.5%
TEST
ING
For
Exe
rcis
es 8
–10,
use
th
e fo
llow
ing
info
rmat
ion
.T
he
aver
age
tim
e it
tak
es s
oph
omor
es t
o co
mpl
ete
a m
ath
tes
t is
nor
mal
ly d
istr
ibu
ted
wit
ha
mea
n o
f 63
.3 m
inu
tes
and
a st
anda
rd d
evia
tion
of
12.3
min
ute
s.
8.A
bout
wha
t pe
rcen
t of
the
sop
hom
ores
tak
e m
ore
than
75.
6 m
inut
es t
o co
mpl
ete
the
test
?16
%9.
Abo
ut
wh
at p
erce
nt
of t
he
soph
omor
es t
ake
betw
een
51
and
63.3
min
ute
s?34
%
10.A
bou
t w
hat
per
cen
t of
th
e so
phom
ores
tak
e le
ss t
han
63.
3 m
inu
tes
to c
ompl
ete
the
test
?50
%
0–3
4–7
8–11
12–1
516
�
20 18 16 14 12 10 8 6 4 2
Frequency
Day
s
Pati
ent
Stay
s
Day
sN
um
ber
of
Pat
ien
ts
0–3
5
4–7
18
8–11
11
12–1
59
16�
6
Sp
eech
es G
iven
Po
litic
al C
and
idat
es
0–5
1
6–11
2
12–1
73
18–2
38
24–2
98
Mile
s R
un
Trac
k Te
am M
emb
ers
0–4
3
5–9
4
10–1
47
15–1
95
20–2
32
©G
lenc
oe/M
cGra
w-H
ill73
8G
lenc
oe A
lgeb
ra 2
Det
erm
ine
wh
eth
er t
he
dat
a in
eac
h t
able
ap
pea
r to
be
pos
itiv
ely
skew
ed,
neg
ati
vely
sk
ewed
,or
nor
ma
lly
dis
trib
ute
d.
1.2.
no
rmal
ly d
istr
ibu
ted
neg
ativ
ely
skew
ed
For
Exe
rcis
es 3
an
d 4
,use
th
e fr
equ
ency
tab
le t
hat
sh
ows
the
nu
mb
er o
f h
ours
wor
ked
per
wee
k b
y 10
0 h
igh
sch
ool
sen
iors
.
3.M
ake
a h
isto
gram
of
the
data
.
4.D
o th
e da
ta a
ppea
r to
be
posi
tive
lysk
ewed
,neg
ativ
ely
skew
ed,o
r n
orm
ally
dis
trib
ute
d?
Exp
lain
.P
osi
tive
ly s
kew
ed;
the
his
tog
ram
is h
igh
at
the
left
an
d h
as a
tai
l to
th
e ri
gh
t.
TEST
ING
For
Exe
rcis
es 5
–10,
use
th
e fo
llow
ing
info
rmat
ion
.T
he
scor
es o
n a
tes
t ad
min
iste
red
to p
rosp
ecti
ve e
mpl
oyee
s ar
e n
orm
ally
dis
trib
ute
d w
ith
am
ean
of
100
and
a st
anda
rd d
evia
tion
of
15.
5.A
bou
t w
hat
per
cen
t of
th
e sc
ores
are
bet
wee
n 7
0 an
d 13
0?95
%
6.A
bou
t w
hat
per
cen
t of
th
e sc
ores
are
bet
wee
n 8
5 an
d 13
0?81
.5%
7.A
bou
t w
hat
per
cen
t of
th
e sc
ores
are
ove
r 11
5?16
%
8.A
bou
t w
hat
per
cen
t of
th
e sc
ores
are
low
er t
han
85
or h
igh
er t
han
115
?32
%
9.If
80
peop
le t
ake
the
test
,how
man
y w
ould
you
exp
ect
to s
core
hig
her
th
an 1
30?
2
10.I
f 75
peo
ple
take
th
e te
st,h
ow m
any
wou
ld y
ou e
xpec
t to
sco
re l
ower
th
an 8
5?12
11.T
EMPE
RA
TUR
ET
he
dail
y Ju
ly s
urf
ace
tem
pera
ture
of
a la
ke a
t a
reso
rt h
as a
mea
n o
f82
�an
d a
stan
dard
dev
iati
on o
f 4.
2�.I
f yo
u p
refe
r to
sw
im w
hen
th
e te
mpe
ratu
re i
s at
leas
t 77
.8�,
abou
t w
hat
per
cen
t of
th
e da
ys d
oes
the
tem
pera
ture
mee
t yo
ur
pref
eren
ce?
84%
0–8
9–17
18–2
526
�
60 50 40 30 20 10Frequency
Ho
urs
Wee
kly
Wo
rk H
ou
rs
Ho
urs
Nu
mb
er o
f S
tud
ents
0–8
30
9–17
45
18–2
520
26�
5
Ave
rag
e A
ge
of
Hig
h S
cho
ol P
rin
cip
als
Ag
e in
Yea
rsN
um
ber
31–3
53
36–4
08
41–4
515
46–5
032
51–5
540
56–6
038
60�
4
Tim
e S
pen
t at
a M
use
um
Exh
ibit
Min
ute
sF
req
uen
cy
0–25
27
26–5
046
51–7
589
75–1
0057
100�
24
Pra
ctic
e (
Ave
rag
e)
Th
e N
orm
al D
istr
ibu
tio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-7
12-7
© Glencoe/McGraw-Hill A22 Glencoe Algebra 2
Answers (Lesson 12-7)
Readin
g t
o L
earn
Math
em
ati
csT
he
No
rmal
Dis
trib
uti
on
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-7
12-7
©G
lenc
oe/M
cGra
w-H
ill73
9G
lenc
oe A
lgeb
ra 2
Lesson 12-7
Pre-
Act
ivit
yH
ow a
re t
he
hei
ghts
of
pro
fess
ion
al a
thle
tes
dis
trib
ute
d?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 12
-7 a
t th
e to
p of
pag
e 67
1 in
you
r te
xtbo
ok.
Th
ere
wer
e 53
pla
yers
on
th
e te
am a
nd
the
mea
n h
eigh
t w
as a
ppro
xim
atel
y73
.6.A
bou
t w
hat
fra
ctio
n o
f th
e pl
ayer
s’ h
eigh
ts a
re b
etw
een
72
and
75,
incl
usi
ve?
Sam
ple
an
swer
:ab
ou
t �2 3�
Rea
din
g t
he
Less
on
1.In
dica
te w
het
her
eac
h o
f th
e fo
llow
ing
stat
emen
ts i
s tr
ue
or f
alse
.
a.In
a c
onti
nu
ous
prob
abil
ity
dist
ribu
tion
,th
ere
is a
fin
ite
nu
mbe
r of
pos
sibl
e ou
tcom
es.
fals
e
b.
Eve
ry n
orm
al d
istr
ibu
tion
can
be
repr
esen
ted
by a
bel
l cu
rve.
tru
e
c.A
dis
trib
uti
on t
hat
is
repr
esen
ted
by a
cu
rve
that
is
hig
h a
t th
e le
ft a
nd
has
a t
ail
toth
e ri
ght
is n
egat
ivel
y sk
ewed
.fa
lse
d.
A n
orm
al d
istr
ibu
tion
is
an e
xam
ple
of a
ske
wed
dis
trib
uti
on.
fals
e
2.M
s.R
ose
gave
the
sam
e qu
iz t
o he
r tw
o ge
omet
ry c
lass
es.S
he r
ecor
ded
the
follo
win
g sc
ores
.
Fir
st-p
erio
d c
lass
:
Fif
th-p
erio
d c
lass
:
In e
ach
cla
ss,3
0 st
ude
nts
too
k th
e qu
iz.T
he
mea
n s
core
for
eac
h c
lass
was
6.4
.Wh
ich
set
of s
core
s h
as t
he
grea
ter
stan
dard
dev
iati
on?
(An
swer
th
is q
ues
tion
wit
hou
t do
ing
any
calc
ula
tion
s.)
Exp
lain
you
r an
swer
.
Fir
st p
erio
d c
lass
;sa
mp
le a
nsw
er:T
he
sco
res
are
mo
re s
pre
ad o
ut
fro
mth
e m
ean
th
an f
or
the
fift
h p
erio
d c
lass
.
Hel
pin
g Y
ou
Rem
emb
er
3.M
any
stu
den
ts h
ave
trou
ble
rem
embe
rin
g h
ow t
o de
term
ine
if a
cu
rve
repr
esen
ts a
dist
ribu
tion
th
at i
s po
siti
vely
ske
wed
or n
egat
ivel
y sk
ewed
.Wh
at i
s an
eas
y w
ay t
ore
mem
ber
this
?
Sam
ple
an
swer
:F
ollo
w t
he
tail!
If t
he
tail
is o
n t
he
rig
ht
(po
siti
ved
irec
tio
n),
the
dis
trib
uti
on
is p
osi
tive
ly s
kew
ed.I
f th
e ta
il is
on
th
e le
ft(n
egat
ive
dir
ecti
on
),th
e d
istr
ibu
tio
n is
neg
ativ
ely
skew
ed.
Sco
re0
12
34
56
78
910
Fre
qu
ency
00
00
34
97
61
0
Sco
re0
12
34
56
78
910
Fre
qu
ency
10
10
34
57
43
2
©G
lenc
oe/M
cGra
w-H
ill74
0G
lenc
oe A
lgeb
ra 2
Str
eet
Net
wo
rks:
Fin
din
g A
ll P
oss
ible
Ro
ute
sA
sec
tion
of
a ci
ty i
s la
id o
ut
in s
quar
e bl
ocks
.Goi
ng
nor
th f
rom
th
e in
ters
ecti
on o
f F
irst
Ave
nu
e an
d F
irst
S
tree
t,th
e av
enu
es a
re 1
st,2
nd,
3rd,
and
so o
n.G
oin
g ea
st,t
he
stre
ets
are
nu
mbe
red
in t
he
sam
e w
ay.
Fact
oria
ls c
an b
e u
sed
to f
ind
the
nu
mbe
r,r(
e,n
),of
di
ffer
ent
rou
tes
betw
een
tw
o in
ters
ecti
ons.
Th
e fo
rmu
la
is s
how
n b
elow
.
r(e,
n)
�
The
num
ber
of s
tree
ts g
oing
eas
t is
e;t
he n
umbe
r of
av
enue
s go
ing
nort
h is
n.
Th
e fo
llow
ing
prob
lem
s ex
amin
e th
e po
ssib
le r
oute
s fr
om o
ne
loca
tion
to
an
oth
er.A
ssu
me
that
you
nev
er u
se a
rou
te t
hat
is
un
nec
essa
rily
lon
g.A
ssu
me
that
e
1 an
d n
1.
Sol
ve e
ach
pro
ble
m.
1.L
ist
all
the
poss
ible
rou
tes
from
1st
Str
eet
and
1st
Ave
nu
e to
4th
Str
eet
and
3rd
Ave
nu
e.U
se o
rder
ed p
airs
to
show
th
e ro
ute
s,w
ith
str
eet
nu
mbe
rs f
irst
,an
d av
enu
e n
um
bers
sec
ond.
For
exa
mpl
e,ea
ch r
oute
star
ts a
t (1
,1)
and
ends
at
(4,3
).
(1,1
) �
(2,1
) �
(3,1
) �
(4,1
) �
(4,2
) �
(4,3
)(1
,1)
�(2
,1)
�(3
,1)
�(3
,2)
�(4
,2)
�(4
,3)
(1,1
) �
(2,1
) �
(3,1
) �
(3,2
) �
(3,3
) �
(4,3
)(1
,1)
�(2
,1)
�(2
,2)
�(3
,2)
�(4
,2)
�(4
,3)
(1,1
) �
(2,1
) �
(2,2
) �
(3,2
) �
(3,3
) �
(4,3
)(1
,1)
�(2
,1)
�(2
,2)
�(2
,3)
�(3
,3)
�(4
,3)
(1,1
) �
(1,2
) �
(2,2
) �
(3,2
) �
(4,2
) �
(4,3
)(1
,1)
�(1
,2)
�(2
,2)
�(3
,2)
�(3
,3)
�(4
,3)
(1,1
) �
(1,2
) �
(2,2
) �
(2,3
) �
(3,3
) �
(4,3
)(1
,1)
�(1
,2)
�(1
,3)
�(2
,3)
�(3
,3)
�(4
,3)
2.U
se t
he
form
ula
to
com
pute
th
e n
um
ber
of r
oute
s fr
om (
1,1)
to
(4,3
).T
her
e ar
e 4
stre
ets
goin
g ea
st a
nd
3 av
enu
es g
oin
g n
orth
.
�(33� !2
2 !)!�
�10
3.F
ind
the
nu
mbe
r of
rou
tes
from
1st
Str
eet
and
1st
Ave
nu
e to
7th
Str
eet
and
6th
Ave
nu
e.
�(66� !5
5 !)!�
�46
2
[(e
�1)
�(n
�1)
]!�
��
(e�
1)!(
n�
1)!
6th
Ave
5th
Ave
4th
Ave
3rd
Ave
2nd
Ave
1st A
ve
1st St.
2nd St.
3rd St.
4th St.
5th St.
6th St.
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-7
12-7
© Glencoe/McGraw-Hill A23 Glencoe Algebra 2
An
swer
s
Answers (Lesson 12-8)
Stu
dy G
uid
e a
nd I
nte
rven
tion
Bin
om
ial E
xper
imen
ts
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-8
12-8
©G
lenc
oe/M
cGra
w-H
ill74
1G
lenc
oe A
lgeb
ra 2
Lesson 12-8
Bin
om
ial E
xpan
sio
ns
For
sit
uat
ion
s w
ith
on
ly 2
pos
sibl
e ou
tcom
es,y
ou c
an u
se t
he
Bin
omia
l Th
eore
m t
o fi
nd
prob
abil
itie
s.T
he
coef
fici
ents
of
term
s in
a b
inom
ial
expa
nsi
onca
n b
e fo
un
d by
usi
ng
com
bin
atio
ns.
Wh
at i
s th
e p
rob
abil
ity
that
3 c
oin
s sh
ow h
ead
s an
d 3
sh
ow t
ails
wh
en 6
coi
ns
are
toss
ed?
Th
ere
are
2 po
ssib
le o
utc
omes
th
at a
re e
qual
ly l
ikel
y:h
eads
(H
) an
d ta
ils
(T).
Th
e to
sses
of
6 co
ins
are
inde
pen
den
t ev
ents
.Wh
en (
H �
T)6
is e
xpan
ded,
the
term
con
tain
ing
H3 T
3 ,w
hic
h r
epre
sen
ts 3
hea
ds a
nd
3 ta
ils,
is u
sed
to g
et t
he
desi
red
prob
abil
ity.
By
the
Bin
omia
lT
heo
rem
th
e co
effi
cien
t of
H3 T
3is
C(6
,3).
P(3
hea
ds,3
tai
ls)
�� 36 !3! !
���1 2� �3 ��1 2� �3
P(H
) �
�1 2�an
d P
(T)
��1 2�
��2 60 4�
�� 15 6�
Th
e pr
obab
ilit
y of
get
tin
g 3
hea
ds a
nd
3 ta
ils
is � 15 6�
or 0
.312
5.
Fin
d e
ach
pro
bab
ilit
y if
a c
oin
is
toss
ed 8
tim
es.
1.P
(exa
ctly
5 h
eads
) 2.
P(e
xact
ly 2
hea
ds)
abo
ut
22%
abo
ut
11%
3.P
(eve
n n
um
ber
of h
eads
) 4.
P(a
t le
ast
6 h
eads
)
50%
abo
ut
14%
Mik
e gu
esse
s on
all
10
qu
esti
ons
of a
tru
e-fa
lse
test
.If
the
answ
ers
tru
e an
d f
alse
are
even
ly d
istr
ibu
ted
,fin
d e
ach
pro
bab
ilit
y.
5.M
ike
gets
exa
ctly
8 c
orre
ct a
nsw
ers.
6.M
ike
gets
at
mos
t 3
corr
ect
answ
ers.
or
0.04
4o
r 0.
172
7.A
die
is
toss
ed 4
tim
es.W
hat
is
the
prob
abil
ity
of t
ossi
ng
exac
tly
two
sixe
s?
or
0.11
625 � 21
6
11 � 6445
� 1024
Exam
ple
Exam
ple
Exer
cises
Exer
cises
©G
lenc
oe/M
cGra
w-H
ill74
2G
lenc
oe A
lgeb
ra 2
Bin
om
ial E
xper
imen
ts
Abi
nom
ial e
xper
imen
t is
pos
sibl
e if
and
only
if a
ll of
the
se c
ondi
tions
occ
ur.
•T
here
are
exa
ctly
tw
o ou
tcom
es f
or e
ach
tria
l.B
ino
mia
l Exp
erim
ents
•T
here
is a
fix
ed n
umbe
r of
tria
ls.
•T
he t
rials
are
inde
pend
ent.
•T
he p
roba
bilit
ies
for
each
tria
l are
the
sam
e.
Su
pp
ose
a co
in i
s w
eigh
ted
so
that
th
e p
rob
abil
ity
of g
etti
ng
hea
ds
inan
y on
e to
ss i
s 90
%.W
hat
is
the
pro
bab
ilit
y of
get
tin
g ex
actl
y 7
hea
ds
in 8
tos
ses?
Th
e pr
obab
ilit
y of
get
tin
g h
eads
is
� 19 0�,a
nd
the
prob
abil
ity
of g
etti
ng
tail
s is
� 11 0�.T
her
e ar
eC
(8,7
) w
ays
to c
hoo
se t
he
7 h
eads
.
P(7
hea
ds)
�C
(8,7
) ��7 �
�1
�8
�
�0.
38
Th
e pr
obab
ilit
y of
get
tin
g 7
hea
ds i
n 8
tos
ses
is a
bou
t 38
%.
1.B
ASK
ETB
ALL
For
an
y on
e fo
ul
shot
,Der
ek h
as a
pro
babi
lity
of
0.72
of
gett
ing
the
shot
in t
he
bask
et.A
s pa
rt o
f a
prac
tice
dri
ll,h
e sh
oots
8 s
hot
s fr
om t
he
fou
l li
ne.
a.W
hat
is
the
prob
abil
ity
that
he
gets
in
exa
ctly
6 f
oul
shot
s? a
bo
ut
31%
b.W
hat
is
the
prob
abil
ity
that
he
gets
in
at
leas
t 6
fou
l sh
ots?
ab
ou
t 60
%
2.SC
HO
OL
A t
each
er i
s tr
yin
g to
dec
ide
wh
eth
er t
o h
ave
4 or
5 c
hoi
ces
per
ques
tion
on
her
mu
ltip
le c
hoi
ce t
est.
Sh
e w
ants
to
prev
ent
stu
den
ts w
ho
just
gu
ess
from
sco
rin
g w
ell
on t
he
test
.
a.O
n a
5-q
ues
tion
mu
ltip
le-c
hoi
ce t
est
wit
h 4
ch
oice
s pe
r qu
esti
on,w
hat
is
the
prob
abil
ity
that
a s
tude
nt
can
sco
re a
t le
ast
60%
by
gues
sin
g? 1
0.4%
b.W
hat
is
the
prob
abil
ity
that
a s
tude
nt
can
sco
re a
t le
ast
60%
by
gues
sin
g on
a t
est
ofth
e sa
me
len
gth
wit
h 5
ch
oice
s pe
r qu
esti
on?
5.8%
3.Ju
lie
roll
s tw
o di
ce a
nd
adds
th
e tw
o n
um
bers
.
a.W
hat
is
the
prob
abil
ity
that
th
e su
m w
ill
be d
ivis
ible
by
3? �1 3�
b.I
f sh
e ro
lls
the
dice
5 t
imes
wh
at i
s th
e ch
ance
th
at s
he
wil
l ge
t ex
actl
y 3
sum
s th
atar
e di
visi
ble
by 3
? ab
ou
t 16
%
4.SK
ATI
NG
Du
rin
g pr
acti
ce a
ska
ter
fall
s 15
% o
f th
e ti
me
wh
en p
ract
icin
g a
trip
le a
xel.
Du
rin
g on
e pr
acti
ce s
essi
on h
e at
tem
pts
20 t
ripl
e ax
els.
a.W
hat
is
the
prob
abil
ity
that
he
wil
l fa
ll o
nly
on
ce?
abo
ut
14%
b.W
hat
is
the
prob
abil
ity
that
he
wil
l fa
ll 4
tim
es?
abo
ut
18%
97� 10
8
1 � 109 � 10
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Bin
om
ial E
xper
imen
ts
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-8
12-8
Exam
ple
Exam
ple
Exer
cises
Exer
cises
© Glencoe/McGraw-Hill A24 Glencoe Algebra 2
Answers (Lesson 12-8)
Skil
ls P
ract
ice
Bin
om
ial E
xper
imen
ts
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-8
12-8
©G
lenc
oe/M
cGra
w-H
ill74
3G
lenc
oe A
lgeb
ra 2
Lesson 12-8
Fin
d e
ach
pro
bab
ilit
y if
a c
oin
is
toss
ed 4
tim
es.
1.P
(4 h
eads
)� 11 6�
2.P
(0 h
eads
)� 11 6�
3.P
(exa
ctly
3 h
eads
)�1 4�
4.P
(exa
ctly
2 h
eads
)�3 8�
5.P
(exa
ctly
1 h
ead)
�1 4�6.
P(a
t le
ast
3 h
eads
)� 15 6�
Fin
d e
ach
pro
bab
ilit
y if
a d
ie i
s ro
lled
3 t
imes
.
7.P
(exa
ctly
on
e 2)
�2 75 2�8.
P(e
xact
ly t
wo
2s)
� 75 2�
9.P
(exa
ctly
th
ree
2s)
� 21 16�10
.P(a
t m
ost
one
2)�2 25 7�
A t
own
th
at p
rese
nts
a f
irew
ork
s d
isp
lay
du
rin
g it
s J
uly
4 c
eleb
rati
on f
oun
d t
he
pro
bab
ilit
y th
at a
fam
ily
wit
h t
wo
or m
ore
chil
dre
n w
ill
wat
ch t
he
fire
wor
ks
is �3 5� .
If 5
of
thes
e fa
mil
ies
are
sele
cted
at
ran
dom
,fin
d e
ach
pro
bab
ilit
y.
11.P
(exa
ctly
3 f
amil
ies
wat
ch t
he
fire
wor
ks)
12.P
(exa
ctly
2 f
amil
ies
wat
ch t
he
fire
wor
ks)
�2 61 26 5��1 64 24 5�
13.P
(exa
ctly
5 f
amil
ies
wat
ch t
he
fire
wor
ks)
14.P
(no
fam
ilie
s w
atch
th
e fi
rew
orks
)
� 32 14 23 5�
� 33 12 25�
15.P
(at
leas
t 4
fam
ilie
s w
atch
th
e fi
rew
orks
)16
.P(a
t m
ost
1 fa
mil
y w
atch
es t
he
fire
wor
ks)
�1 30 15 23 5�
� 32 17 22 5�
On
e se
ctio
n o
f a
stan
dar
diz
ed E
ngl
ish
lan
guag
e te
st h
as 1
0 tr
ue/
fals
e q
ues
tion
s.F
ind
eac
h p
rob
abil
ity
wh
en a
stu
den
t gu
esse
s at
all
ten
qu
esti
ons.
17.P
(exa
ctly
8 c
orre
ct)
� 14 05 24�18
.P(e
xact
ly 2
cor
rect
)� 14 05 24�
19.P
(exa
ctly
hal
f co
rrec
t)� 26 53 6�
20.P
(all
10
corr
ect)
� 101 24�
21.P
(0 c
orre
ct)
� 101 24�
22.P
(at
leas
t 8
corr
ect)
� 17 28�
©G
lenc
oe/M
cGra
w-H
ill74
4G
lenc
oe A
lgeb
ra 2
Fin
d e
ach
pro
bab
ilit
y if
a c
oin
is
toss
ed 6
tim
es.
1.P
(exa
ctly
3 t
ails
)� 15 6�
2.P
(exa
ctly
5 t
ails
)� 33 2�
3.P
(0 t
ails
)� 61 4�
4.P
(at
leas
t 4
hea
ds)
�1 31 2�
5.P
(at
leas
t 4
tail
s)�1 31 2�
6.P
(at
mos
t 2
tail
s)�1 31 2�
Th
e p
rob
abil
ity
of C
hri
s m
akin
g a
free
th
row
is
�2 3� .If
sh
e sh
oots
5 t
imes
,fin
d e
ach
pro
bab
ilit
y.
7.P
(all
mis
sed)
� 21 43�8.
P(a
ll m
ade)
� 23 42 3�
9.P
(exa
ctly
2 m
ade)
� 24 40 3�10
.P(e
xact
ly 1
mis
sed)
� 28 40 3�
11.P
(at
leas
t 3
mad
e)�6 84 1�
12.P
(at
mos
t 2
mad
e)�1 87 1�
Wh
en T
arin
an
d S
am p
lay
a ce
rtai
n b
oard
gam
e,th
e p
rob
abil
ity
that
Tar
in w
ill
win
a
gam
e is
�3 4� .If
th
ey p
lay
5 ga
mes
,fin
d e
ach
pro
bab
ilit
y.
13.P
(Sam
win
s on
ly o
nce
)� 14 00 25 4
�14
.P(T
arin
win
s ex
actl
y tw
ice)
� 54 15 2�
15.P
(Sam
win
s ex
actl
y 3
gam
es)
� 54 15 2�16
.P(S
am w
ins
at l
east
1 g
ame)
� 17 08 21 4�
17.P
(Tar
in w
ins
at l
east
3 g
ames
)�4 55 19 2�
18.P
(Tar
in w
ins
at m
ost
2 ga
mes
)� 55 13 2�
19.S
AFE
TYIn
Au
gust
200
1,th
e A
mer
ican
Au
tom
obil
e A
ssoc
iati
on r
epor
ted
that
73%
of
Am
eric
ans
use
sea
t be
lts.
In a
ran
dom
sel
ecti
on o
f 10
Am
eric
ans
in 2
001,
wh
at i
s th
epr
obab
ilit
y th
at e
xact
ly h
alf
of t
hem
use
sea
t be
lts?
Sour
ce:A
AAab
ou
t 7.
5%
HEA
LTH
For
Exe
rcis
es 2
0 an
d 2
1,u
se t
he
foll
owin
g in
form
atio
n.
In 2
001,
the
Am
eric
an H
eart
Ass
ocia
tion
rep
orte
d th
at 5
0 pe
rcen
t of
th
e A
mer
ican
s w
ho
rece
ive
hear
t tr
ansp
lant
s ar
e ag
es 5
0–64
and
20
perc
ent
are
ages
35–
49.
Sour
ce: A
mer
ican
Hear
t Ass
ociat
ion
20.I
n a
ran
dom
ly s
elec
ted
grou
p of
10
hea
rt t
ran
spla
nt
reci
pien
ts,w
hat
is
the
prob
abil
ity
that
at
leas
t 8
of t
hem
are
age
s 50
–64?
� 17 28�
21.I
n a
ran
dom
ly s
elec
ted
grou
p of
5 h
eart
tra
nsp
lan
t re
cipi
ents
,wh
at i
s th
e pr
obab
ilit
yth
at 2
of
them
are
age
s 35
–49?
�1 62 28 5�
Pra
ctic
e (
Ave
rag
e)
Bin
om
ial E
xper
imen
ts
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-8
12-8
© Glencoe/McGraw-Hill A25 Glencoe Algebra 2
An
swer
s
Answers (Lesson 12-8)
Readin
g t
o L
earn
Math
em
ati
csB
ino
mia
l Exp
erim
ents
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-8
12-8
©G
lenc
oe/M
cGra
w-H
ill74
5G
lenc
oe A
lgeb
ra 2
Lesson 12-8
Pre-
Act
ivit
yH
ow c
an y
ou d
eter
min
e w
het
her
gu
essi
ng
is w
orth
it?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 12
-8 a
t th
e to
p of
pag
e 67
6 in
you
r te
xtbo
ok.
Su
ppos
e yo
u a
re t
akin
g a
50-q
ues
tion
mu
ltip
le-c
hoi
ce t
est
in w
hic
h t
her
ear
e 5
answ
er c
hoi
ces
for
each
qu
esti
on.Y
ou a
re t
old
that
no
poin
ts w
ill
bede
duct
ed f
or w
ron
g an
swer
s.S
hou
ld y
ou g
ues
s th
e an
swer
s to
th
e qu
esti
ons
you
do
not
kn
ow?
Exp
lain
you
r re
ason
ing.
Sam
ple
an
swer
:Yes
;th
e p
rob
abili
ty o
f g
ues
sin
g t
he
rig
ht
answ
er t
o a
qu
esti
on
is �1 5� ,
so
you
hav
e a
chan
ce t
o g
et s
om
e p
oin
ts b
y g
ues
sin
g,a
nd
yo
uh
ave
no
thin
g t
o lo
se.
Rea
din
g t
he
Less
on
1.In
dica
te w
het
her
eac
h o
f th
e fo
llow
ing
is a
bin
omia
l ex
peri
men
tor
not
a b
inom
ial
expe
rim
ent.
If t
he
expe
rim
ent
is n
ot a
bin
omia
l ex
peri
men
t,ex
plai
n w
hy.
a.A
fai
r co
in i
s to
ssed
10
tim
es a
nd
“hea
ds”
or “
tail
s”is
rec
orde
d ea
ch t
ime.
bin
om
ial
exp
erim
ent
b.
A p
air
of d
ice
is t
hro
wn
5 t
imes
an
d th
e su
m o
f th
e n
um
bers
th
at c
ome
up
is r
ecor
ded
each
tim
e.N
ot
a b
ino
mia
l exp
erim
ent;
ther
e ar
e m
ore
th
an t
wo
po
ssib
leo
utc
om
es f
or
each
tri
al.
c.T
her
e ar
e 5
red
mar
bles
an
d 6
blu
e m
arbl
es i
n a
bag
.On
e m
arbl
e is
dra
wn
fro
m t
he
bag
and
its
colo
r re
cord
ed.T
he
mar
ble
is n
ot p
ut
back
in
th
e ba
g.A
sec
ond
mar
ble
isdr
awn
an
d it
s co
lor
reco
rded
.N
ot
a b
ino
mia
l exp
erim
ent;
the
tria
ls a
re n
ot
ind
epen
den
t (o
r,th
e p
rob
abili
ties
fo
r th
e tw
o t
rial
s ar
e n
ot
the
sam
e).
d.
Th
ere
are
5 re
d m
arbl
es a
nd
6 bl
ue
mar
bles
in
a b
ag.O
ne
mar
ble
is d
raw
n f
rom
th
eba
g an
d it
s co
lor
reco
rded
.Th
e m
arbl
e is
pu
t ba
ck i
n t
he
bag.
A s
econ
d m
arbl
e is
draw
n a
nd
its
colo
r re
cord
ed.
bin
om
ial e
xper
imen
t
2.L
en r
ando
mly
gu
esse
s th
e an
swer
s to
all
6 m
ult
iple
-ch
oice
qu
esti
ons
on h
is c
hem
istr
yte
st.E
ach
qu
esti
on h
as 5
ch
oice
s.W
hic
h o
f th
e fo
llow
ing
expr
essi
ons
give
s th
epr
obab
ilit
y th
at h
e w
ill
get
at l
east
4 o
f th
e an
swer
s co
rrec
t?B
A.
P(6
,4) ��1 5� �4 ��4 5� �2
�P
(6,5
) ��1 5� �5 ��4 5� �1�
P(6
,6) ��1 5� �6 ��4 5� �0
B.C
(6,4
) ��1 5� �4 ��4 5� �2�
C(6
,5) ��1 5� �5 ��4 5� �1
�C
(6,6
) ��1 5� �6 ��4 5� �0
C.
C(6
,4) ��1 5� �2 ��4 5� �4
�C
(6,5
) ��1 5� �1 ��4 5� �5�
C(6
,6) ��1 5� �0 ��4 5� �6
Hel
pin
g Y
ou
Rem
emb
er3.
Som
e st
uden
ts h
ave
trou
ble
rem
embe
ring
how
to
calc
ulat
e bi
nom
ial
prob
abil
itie
s.W
hat
is
an e
asy
way
to
rem
embe
r w
hic
h n
um
bers
to
put
into
an
exp
ress
ion
lik
e C
(6,4
) ��1 5� �2 ��4 5� �4?
Sam
ple
an
swer
:Th
e b
ino
mia
l co
effi
cien
t is
C(n
,r),
wh
ere
nis
th
e n
um
ber
of
tria
ls a
nd
ris
th
e n
um
ber
of
succ
esse
s.T
he
pro
bab
ility
of
succ
ess
isra
ised
to
th
e rt
h p
ow
er a
nd
th
e p
rob
abili
ty o
f fa
ilure
is r
aise
d t
o t
he
(n�
r)th
po
wer
.
©G
lenc
oe/M
cGra
w-H
ill74
6G
lenc
oe A
lgeb
ra 2
Mis
use
s o
f S
tati
stic
sS
tati
stic
s ca
n b
e m
isle
adin
g.G
raph
s fo
r a
set
of d
ata
can
loo
k ve
ry d
iffe
ren
tfr
om o
ne
anot
her
.Com
pare
th
e fo
llow
ing
grap
hs.
Not
ice
that
th
e tw
o gr
aph
s sh
ow t
he
sam
e da
ta,b
ut
the
spac
ing
in t
he
vert
ical
an
d h
oriz
onta
l sc
ales
dif
fers
.Sca
les
can
be
cram
ped
or s
prea
d ou
t to
mak
e a
grap
h t
hat
giv
es a
cer
tain
im
pres
sion
.Wh
ich
gra
ph w
ould
you
use
to
give
th
e im
pres
sion
th
at t
he
un
empl
oym
ent
rate
dro
pped
dra
mat
ical
ly f
rom
1990
to
2000
?th
e se
con
d g
rap
h
Su
ppos
e th
at a
car
com
pan
y cl
aim
s,“7
5% o
f pe
ople
su
rvey
ed s
ay t
hat
ou
r ca
ris
bet
ter
than
th
e co
mpe
titi
on.”
If f
our
peop
le w
ere
aske
d w
hic
h c
ar t
hey
pref
erre
d an
d 75
% a
gree
d,h
ow m
any
peop
le t
hou
ght
that
Ou
r C
arw
asbe
tter
?3
peo
ple
Th
e ad
vert
isem
ent
was
mis
lead
ing
in o
ther
way
s as
wel
l.F
or e
xam
ple,
wh
ow
as s
urv
eyed
—w
ere
the
peop
le c
ompa
ny
empl
oyee
s,or
im
part
ial
buye
rs?
Su
pp
ose
an a
dve
rtis
er c
laim
s th
at 9
0% o
f al
l of
on
e b
ran
d o
f ca
r so
ldin
th
e la
st 1
0 ye
ars
are
stil
l on
th
e ro
ad.
1.If
10,
000
cars
wer
e so
ld,h
ow m
any
are
stil
l on
th
e ro
ad?
9,00
0
2.If
100
0 ca
rs w
ere
sold
,how
man
y ar
e st
ill
on t
he
road
?90
0
3.F
ind
an e
xam
ple
to s
how
how
you
th
ink
aver
ages
cou
ld b
e u
sed
in a
mis
lead
ing
way
.S
ee s
tud
ents
’wo
rk.
4.A
su
rvey
of
a la
rge
sam
ple
of p
eopl
e w
ho
own
sm
all
com
pute
rs r
evea
led
that
85%
of
the
peop
le t
hou
ght
the
inst
ruct
ion
man
ual
s sh
ould
be
bett
erw
ritt
en.A
man
ufa
ctu
rer
of s
mal
l co
mpu
ters
cla
imed
th
at i
t su
rvey
edm
any
of t
he
sam
e pe
ople
an
d fo
un
d th
at a
ll o
f th
em l
iked
th
eir
man
ual
s.D
iscu
ss t
he
poss
ible
dis
crep
ancy
in
th
e re
sult
s.S
ee s
tud
ents
’wo
rk.
U.S
. Un
emp
loym
ent
Rat
e
Year
Percent
0’9
0’9
2’9
4’9
6’0
2’9
8’0
0
8 7 6 5 4
Sour
ce: U
.S. D
epar
tmen
t of L
abor
U.S
. Un
emp
loym
ent
Rat
e
Year
Percent
0’9
0’9
2’9
4’9
6’0
2’9
8’0
0’9
1’9
3’9
5’9
7’9
9’0
1
8 7 6 5 4
Sour
ce: U
.S. D
epar
tmen
t of L
abor
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-8
12-8
© Glencoe/McGraw-Hill A26 Glencoe Algebra 2
Answers (Lesson 12-9)
Stu
dy G
uid
e a
nd I
nte
rven
tion
Sam
plin
g a
nd
Err
or
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-9
12-9
©G
lenc
oe/M
cGra
w-H
ill74
7G
lenc
oe A
lgeb
ra 2
Lesson 12-9
Bia
sA
sam
ple
of s
ize
nis
ran
dom
(or
un
bia
sed
) w
hen
eve
ry p
ossi
ble
sam
ple
of s
ize
nh
asan
equ
al c
han
ce o
f be
ing
sele
cted
.If
a sa
mpl
e is
bia
sed,
then
in
form
atio
n o
btai
ned
fro
m i
tm
ay n
ot b
e re
liab
le.
To
fin
d o
ut
how
peo
ple
in
th
e U
.S.f
eel
abou
t m
ass
tran
sit,
peo
ple
at
a co
mm
ute
r tr
ain
sta
tion
are
ask
ed t
hei
r op
inio
n.D
oes
this
sit
uat
ion
rep
rese
nt
ara
nd
om s
amp
le?
No;
the
sam
ple
incl
ude
s on
ly p
eopl
e w
ho
actu
ally
use
a m
ass-
tran
sit
faci
lity
.Th
e sa
mpl
edo
es n
ot i
ncl
ude
peo
ple
wh
o ri
de b
ikes
,dri
ve c
ars,
or w
alk.
Det
erm
ine
wh
eth
er e
ach
sit
uat
ion
wou
ld p
rod
uce
a r
and
om s
amp
le.W
rite
yes
orn
oan
d e
xpla
in y
our
answ
er.
1.as
kin
g pe
ople
in
Ph
oen
ix,A
rizo
na,
abou
t ra
infa
ll t
o de
term
ine
the
aver
age
rain
fall
for
the
Un
ited
Sta
tes
No
;it
rai
ns
less
in P
ho
enix
th
an m
ost
pla
ces
in t
he
U.S
.
2.ob
tain
ing
the
nam
es o
f tr
ee t
ypes
in
Nor
th A
mer
ica
by s
urv
eyin
g al
l of
th
e U
.S.N
atio
nal
For
ests
Yes
;th
ere
are
Nat
ion
al F
ore
sts
in a
bo
ut
ever
y st
ate
in t
he
U.S
.
3.su
rvey
ing
ever
y te
nth
per
son
wh
o en
ters
th
e m
all
to f
ind
out
abou
t m
usi
c pr
efer
ence
s in
that
par
t of
th
e co
un
try
Yes;
mal
l cu
sto
mer
s sh
ou
ld b
e fa
irly
rep
rese
nta
tive
in t
erm
s o
f m
usi
c ta
stes
.
4.in
terv
iew
ing
cou
ntr
y cl
ub
mem
bers
to
dete
rmin
e th
e av
erag
e n
um
ber
of t
elev
isio
ns
per
hou
seh
old
in t
he
com
mu
nit
y N
o;
cou
ntr
y cl
ub
mem
ber
s w
ou
ld t
end
to
be
mo
re a
fflu
ent
and
th
us
no
t a
rep
rese
nta
tive
sam
ple
of
the
com
mu
nit
y.
5.su
rvey
ing
all
stu
den
ts w
hos
e ID
nu
mbe
rs e
nd
in 4
abo
ut
thei
r gr
ades
an
d ca
reer
coun
seli
ng n
eeds
Yes
;ID
nu
mb
ers
are
pro
bab
ly a
ssig
ned
alp
hab
etic
ally
or
byso
me
othe
r m
etho
d no
t co
nnec
ted
to s
tude
nts’
grad
es o
r co
unse
ling
need
s.
6.su
rvey
ing
pare
nts
at
a da
y ca
re f
acil
ity
abou
t th
eir
pref
eren
ces
for
bran
ds o
f ba
by f
ood
for
a m
arke
tin
g ca
mpa
ign
Yes
;ch
oic
e o
f a
day
care
fac
ility
wo
uld
pro
bab
lyn
ot
infl
uen
ce b
aby
foo
d p
refe
ren
ces.
7.as
kin
g pe
ople
in
a l
ibra
ry a
bou
t th
e n
um
ber
of m
agaz
ines
to
wh
ich
th
ey s
ubs
crib
e in
orde
r to
des
crib
e th
e re
adin
g h
abit
s of
a t
own
No
;lib
rary
vis
ito
rs t
end
to
rea
dm
ore
th
an m
ost
cit
izen
s.
Exam
ple
Exam
ple
Exer
cises
Exer
cises
©G
lenc
oe/M
cGra
w-H
ill74
8G
lenc
oe A
lgeb
ra 2
Mar
gin
of
Erro
rT
he
mar
gin
of
sam
pli
ng
erro
rgi
ves
a li
mit
on
th
e di
ffer
ence
betw
een
how
a s
ampl
e re
spon
ds a
nd
how
th
e to
tal
popu
lati
on w
ould
res
pon
d.
If th
e pe
rcen
t of
peo
ple
in a
sam
ple
resp
ondi
ng in
a c
erta
in w
ay is
pan
d th
e si
ze o
f th
e sa
mpl
e M
arg
in o
f E
rro
ris
n,
then
95%
of
the
time,
the
per
cent
of
the
popu
latio
n re
spon
ding
in t
hat
sam
e w
ay w
ill b
e
betw
een
p�
ME
and
p�
ME
, w
here
ME
�2�
.
In a
su
rvey
of
4500
ran
dom
ly s
elec
ted
vot
ers,
62%
fav
ored
can
did
ate
A.W
hat
is
the
mar
gin
of
erro
r?
ME
�2 �
For
mul
a fo
r m
argi
n of
sam
plin
g er
ror
�2�
p
�62
% o
r 0.
62,
n�
4500
�0.
0144
7U
se a
cal
cula
tor.
Th
e m
argi
n o
f er
ror
is a
bou
t 1%
.Th
is m
ean
s th
at t
her
e is
a 9
5% c
han
ce t
hat
th
e pe
rcen
t of
vote
rs f
avor
ing
can
dida
te A
is
betw
een
62
�1
or 6
1% a
nd
62 �
1 or
63%
.
Th
e C
D t
hat
32%
of
teen
ager
s su
rvey
ed p
lan
to
bu
y n
ext
is t
he
late
st f
rom
th
e p
opu
lar
new
gro
up
BF
A.I
f th
e m
argi
n o
f er
ror
of t
he
surv
ey i
s 2%
,h
ow m
any
teen
ager
s w
ere
surv
eyed
?
ME
�2 �
For
mul
a fo
r m
argi
n of
sam
plin
g er
ror
0.02
�2�
M
E�
0.02
, p
�0.
32
0.01
��
Div
ide
each
sid
e by
2.
0.00
01 �
Squ
are
each
sid
e.
n�
Mul
tiply
by
nan
d di
vide
by
0.00
01
n�
2176
2176
tee
nag
ers
wer
e su
rvey
ed.
Fin
d t
he
mar
gin
of
sam
pli
ng
erro
r to
th
e n
eare
st p
erce
nt.
1.p
�45
%,n
�35
02.
p�
12%
,n�
1500
3.p
�86
%,n
�60
0ab
ou
t 5%
abo
ut
2%ab
ou
t 3%
4.A
stu
dy o
f 50
,000
dri
vers
in
In
dian
a,Il
lin
ois,
and
Oh
io s
how
ed t
hat
68%
pre
ferr
ed a
spee
d li
mit
of
75 m
ph o
ver
65 m
ph o
n h
igh
way
s an
d co
un
try
road
s.W
hat
was
th
em
argi
n o
f sa
mpl
ing
erro
r to
th
e n
eare
st t
enth
of
a pe
rcen
t? a
bo
ut
0.4%
0.32
(0.6
8)�
�0.
0001
0.32
(0.6
8)�
� n
0.32
(0.6
8)�
� n
0.32
�(1
�0.
32)
�� n
p(1
�p)
�� n
0.62
�(1
�0.
62)
��
4500
p(1
�p)
�� n
p(1
�p)
�� n
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Sam
plin
g a
nd
Err
or
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-9
12-9
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
© Glencoe/McGraw-Hill A27 Glencoe Algebra 2
An
swer
s
Answers (Lesson 12-9)
Skil
ls P
ract
ice
Sam
plin
g a
nd
Err
or
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-9
12-9
©G
lenc
oe/M
cGra
w-H
ill74
9G
lenc
oe A
lgeb
ra 2
Lesson 12-9
Det
erm
ine
wh
eth
er e
ach
sit
uat
ion
wou
ld p
rod
uce
a r
and
om s
amp
le.W
rite
yes
orn
oan
d e
xpla
in y
our
answ
er.
1.ca
llin
g h
ouse
hol
ds a
t 3:
30 P
.M.o
n T
ues
day
to d
eter
min
e a
poli
tica
l ca
ndi
date
’s s
upp
ort
No
;si
nce
mo
st r
egis
tere
d v
ote
rs a
re li
kely
to
be
at w
ork
at
this
tim
e,th
issa
mp
le w
ou
ld n
ot
be
rep
rese
nta
tive
of
all r
egis
tere
d v
ote
rs.
2.po
llin
g cu
stom
ers
as t
hey
exi
t a
spor
tin
g go
ods
stor
e ab
out
thei
r at
titu
des
abou
t ex
erci
seN
o;
thes
e cu
sto
mer
s ar
e lik
ely
to v
alu
e ex
erci
se m
ore
th
an t
ho
se w
ho
do
no
t sh
op
at
spo
rtin
g g
oo
ds
sto
res,
wh
o a
re n
ot
rep
rese
nte
d in
th
is s
urv
ey.
3.re
cord
ing
the
nu
mbe
r of
sit
-ups
per
form
ed b
y 15
-yea
r ol
d gi
rls
in t
he
hig
h s
choo
ls o
f a
larg
e sc
hoo
l di
stri
ct t
o de
term
ine
the
fitn
ess
of a
ll h
igh
-sch
ool
girl
s in
th
e di
stri
ctN
o;
15-y
ear
old
gir
ls m
ay n
ot
hav
e th
e sa
me
abili
ties
as
18-y
ear
old
sen
iors
,fo
r ex
amp
le.
4.se
lect
ing
two
of a
cit
y’s
20 a
part
men
t bu
ildi
ngs
for
a s
urv
ey t
o de
term
ine
the
desi
re o
fap
artm
ent
dwel
lers
in
th
e ci
ty t
o ow
n a
hom
eN
o;
the
resi
den
ts o
f th
e tw
obu
ildin
gs
sele
cted
mig
ht,
for
exam
ple
,hav
e n
icer
ap
artm
ents
or
be
in a
nic
er a
rea
of
tow
n,a
nd
th
us
wo
uld
no
t w
ell r
epre
sen
t th
e d
esir
es o
fp
eop
le in
oth
er b
uild
ing
s.
5.In
a l
arge
sch
ool
dist
rict
,th
e su
peri
nte
nde
nt
of s
choo
ls i
nte
rvie
ws
two
teac
her
s at
ran
dom
fro
m e
ach
sch
ool
to d
eter
min
e w
het
her
tea
cher
s in
th
e di
stri
ct t
hin
k st
ude
nts
are
assi
gned
too
mu
ch o
r to
o li
ttle
hom
ewor
k.Ye
s;si
nce
a c
ross
sec
tio
n o
fte
ach
ers
fro
m a
ll le
vels
was
sel
ecte
d a
t ra
nd
om
,th
e sa
mp
le s
ho
uld
wel
lre
pre
sen
t th
e p
op
ula
tio
n o
f te
ach
ers
in t
he
dis
tric
t.
6.F
or s
even
con
secu
tive
day
s,on
e h
our
each
in
th
e m
orn
ing,
afte
rnoo
n,a
nd
even
ing,
ever
yte
nth
cu
stom
er w
ho
ente
rs a
mal
l is
ask
ed t
o ch
oose
her
or
his
fav
orit
e st
ore.
Yes;
bec
ause
th
e sa
mp
le is
ch
ose
n o
ver
the
cou
rse
of
a w
ho
le w
eek,
du
rin
gh
ou
rs w
hen
dif
fere
nt
con
sum
er g
rou
ps
sho
p,a
nd
bec
ause
th
e se
lect
ion
is s
yste
mat
ic,t
he
sam
ple
sh
ou
ld w
ell r
epre
sen
t th
e g
ener
al p
op
ula
tio
nth
at s
ho
ps
at t
he
mal
l sto
res.
Fin
d t
he
mar
gin
of
sam
pli
ng
erro
r to
th
e n
eare
st p
erce
nt.
7.p
�85
%,n
�10
0ab
ou
t 7%
8.p
�78
%,n
�10
0ab
ou
t 8%
9.p
�15
%,n
�10
0ab
ou
t 7%
10.p
�37
%,n
�50
0ab
ou
t 4%
11.p
�12
%,n
�50
0ab
ou
t 3%
12.p
�93
%,n
�50
0ab
ou
t 2%
13.p
�23
%,n
�10
00ab
ou
t 3%
14.p
�56
%,n
�10
00ab
ou
t 3%
15.H
EALT
HIn
a r
ecen
t po
ll o
f ci
gare
tte
smok
ers,
67%
of
thos
e su
rvey
ed s
aid
they
had
tri
edto
qu
it s
mok
ing
wit
hin
th
e la
st y
ear.
Th
e m
argi
n o
f er
ror
was
3%
.Abo
ut
how
man
ype
ople
wer
e su
rvey
ed?
abo
ut
983
©G
lenc
oe/M
cGra
w-H
ill75
0G
lenc
oe A
lgeb
ra 2
Det
erm
ine
wh
eth
er e
ach
sit
uat
ion
wou
ld p
rod
uce
a r
and
om s
amp
le.W
rite
yes
orn
oan
d e
xpla
in y
our
answ
er.
1.ca
llin
g ev
ery
twen
tiet
h r
egis
tere
d vo
ter
to d
eter
min
e w
het
her
peo
ple
own
or
ren
t th
eir
hom
es i
n y
our
com
mu
nit
yN
o;
reg
iste
red
vo
ters
may
be
mo
re li
kely
to
be
ho
meo
wn
ers,
cau
sin
g t
he
surv
ey t
o u
nd
erre
pre
sen
t re
nte
rs.
2.pr
edic
tin
g lo
cal
elec
tion
res
ult
s by
pol
lin
g pe
ople
in
eve
ry t
wen
tiet
h r
esid
ence
in
all
th
edi
ffer
ent
nei
ghbo
rhoo
ds o
f yo
ur
com
mu
nit
yYe
s;si
nce
all
nei
gh
bo
rho
od
s ar
ere
pre
sen
ted
pro
po
rtio
nal
ly,t
he
view
s o
f th
e co
mm
un
ity
sho
uld
as
aw
ho
le s
ho
uld
be
wel
l rep
rese
nte
d.
3.to
fin
d ou
t w
hy
not
man
y st
ude
nts
are
usi
ng
the
libr
ary,
a sc
hoo
l’s l
ibra
rian
giv
es a
ques
tion
nai
re t
o ev
ery
ten
th s
tude
nt
ente
rin
g th
e li
brar
yN
o;
she
is p
olli
ng
on
lyth
e st
ud
ents
wh
o a
re c
om
ing
to
th
e lib
rary
,an
d w
ill o
bta
in n
o in
pu
t fr
om
tho
se w
ho
are
n’t
usi
ng
th
e lib
rary
.4.
test
ing
over
all
perf
orm
ance
of
tire
s on
in
ters
tate
hig
hw
ays
only
No
;fo
r ov
eral
lp
erfo
rman
ce,t
ires
sh
ou
ld b
e te
sted
on
man
y ki
nd
s o
f su
rfac
es,a
nd
un
der
man
y ty
pes
of
con
dit
ion
s.5.
sele
ctin
g ev
ery
50th
ham
burg
er f
rom
a f
ast-
food
res
tau
ran
t ch
ain
an
d de
term
inin
g it
sfa
t co
nte
nt
to a
sses
s th
e fa
t co
nte
nt
of h
ambu
rger
s se
rved
in
fas
t-fo
od r
esta
ura
nt
chai
ns
thro
ugh
out
the
cou
ntr
yN
o;
the
sele
cted
ham
burg
ers
are
a ra
nd
om
sam
ple
of
the
ham
burg
ers
serv
ed in
on
e ch
ain
,an
d m
ay r
epre
sen
t th
e fa
t co
nte
nt
for
that
ch
ain
,bu
t w
ill n
ot
nec
essa
rily
rep
rese
nt
the
fat
con
ten
t o
fh
ambu
rger
s se
rved
in o
ther
fas
t-fo
od
res
tau
ran
t ch
ain
s.6.
assi
gnin
g al
l sh
ift
wor
kers
in
a m
anu
fact
uri
ng
plan
t a
un
iqu
e id
enti
fica
tion
nu
mbe
r,an
dth
en p
laci
ng
the
nu
mbe
rs i
n a
hat
an
d dr
awin
g 30
at
ran
dom
to
dete
rmin
e th
e an
nu
alav
erag
e sa
lary
of
the
wor
kers
Yes;
bec
ause
th
e n
um
ber
s ar
e ra
nd
om
ly c
ho
sen
fro
m a
mo
ng
all
shif
t w
ork
ers,
all w
ork
ers
hav
e th
e sa
me
chan
ce o
f b
ein
gse
lect
ed.
Fin
d t
he
mar
gin
of
sam
pli
ng
erro
r to
th
e n
eare
st p
erce
nt.
7.p
�26
%,n
�10
08.
p�
55%
,n�
100
9.p
�75
%,n
�50
0ab
ou
t 9%
abo
ut
10%
abo
ut
4%
10.p
�14
%,n
�50
011
.p�
96%
,n�
1000
12.p
�21
%,n
�10
00ab
ou
t 3%
abo
ut
1%ab
ou
t 3%
13.p
�34
%,n
�10
0014
.p�
49%
,n�
1500
15.p
�65
%,n
�15
00ab
ou
t 3%
abo
ut
3%ab
ou
t 2%
16.C
OM
PUTI
NG
Acc
ordi
ng
to a
pol
l of
500
tee
nag
ers,
43%
sai
d th
at t
hey
use
a p
erso
nal
com
pute
r at
hom
e.W
hat
is
the
mar
gin
of
sam
plin
g er
ror?
abo
ut
4%
17.T
RU
STA
sur
vey
of 6
05 p
eopl
e,ag
es 1
3–33
,sho
ws
that
68%
tru
st t
heir
par
ents
mor
e th
anth
eir
best
fri
ends
to
tell
them
the
tru
th.W
hat
is t
he m
argi
n of
sam
plin
g er
ror?
abo
ut
4%
18.P
RO
DU
CTI
VIT
YA
stu
dy b
y th
e U
niv
ersi
ty o
f Il
lin
ois
in 1
995
show
ed a
n i
ncr
ease
in
prod
uct
ivit
y by
10%
of
the
empl
oyee
s w
ho
wor
e h
eads
ets
and
list
ened
to
mu
sic
of t
hei
rch
oice
wh
ile
they
wer
e w
orki
ng.
Th
e m
argi
n o
f sa
mpl
ing
erro
r fo
r th
e st
udy
was
abo
ut
7%.H
ow m
any
empl
oyee
s pa
rtic
ipat
ed i
n t
he
stu
dy?
abo
ut
76
Pra
ctic
e (
Ave
rag
e)
Sam
plin
g a
nd
Err
or
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-9
12-9
© Glencoe/McGraw-Hill A28 Glencoe Algebra 2
Answers (Lesson 12-9)
Readin
g t
o L
earn
Math
em
ati
csS
amp
ling
an
d E
rro
r
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
12-9
12-9
©G
lenc
oe/M
cGra
w-H
ill75
1G
lenc
oe A
lgeb
ra 2
Lesson 12-9
Pre-
Act
ivit
yH
ow a
re o
pin
ion
pol
ls u
sed
in
pol
itic
al c
amp
aign
s?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 12
-9 a
t th
e to
p of
pag
e 68
2 in
you
r te
xtbo
ok.
Do
you
th
ink
the
resu
lts
of t
he
surv
ey a
bou
t th
e pr
esid
enti
al p
refe
ren
ces
dem
onst
rate
s th
at B
ush
was
act
ual
ly a
hea
d in
Flo
rida
a m
onth
bef
ore
the
elec
tion
? If
th
ere
is n
ot e
nou
gh i
nfo
rmat
ion
giv
en t
o de
term
ine
this
,lis
t at
leas
t tw
o qu
esti
ons
you
wou
ld a
sk a
bou
t th
e su
rvey
th
at w
ould
hel
p yo
ude
term
ine
the
sign
ific
ance
of
the
surv
ey.
Sam
ple
an
swer
:Th
ere
is n
ot
eno
ug
h in
form
atio
n t
o t
ell.
1.H
ow m
any
peo
ple
wer
e su
rvey
ed?
2.H
ow
was
th
e sa
mp
le f
or
the
surv
ey s
elec
ted
? 3
.Wh
at is
th
em
arg
in o
f er
ror
for
this
su
rvey
?
Rea
din
g t
he
Less
on
1.D
eter
min
e w
het
her
eac
h s
itu
atio
n w
ould
pro
duce
a r
ando
m s
ampl
e.W
rite
yes
or n
oan
dex
plai
n y
our
answ
er.
a.as
kin
g al
l th
e cu
stom
ers
at f
ive
rest
aura
nts
on
th
e sa
me
even
ing
how
man
y ti
mes
am
onth
th
ey e
at d
inn
er i
n r
esta
ura
nts
to
dete
rmin
e h
ow o
ften
th
e av
erag
e A
mer
ican
eats
din
ner
in
a r
esta
ura
nts
No
;p
eop
le s
urv
eyed
at
a re
stau
ran
t m
igh
t b
elik
ely
to e
at d
inn
er in
res
tau
ran
ts m
ore
oft
en t
han
oth
er p
eop
le.
b.
putt
ing
the
nam
es o
f al
l sen
iors
at
your
hig
h sc
hool
in a
hat
and
the
n dr
awin
g 20
nam
esfo
r a
surv
ey t
o fi
nd
out
wh
ere
sen
iors
wou
ld l
ike
to h
old
thei
r pr
omYe
s;ev
ery
sen
ior
wo
uld
hav
e an
eq
ual
ch
ance
of
bei
ng
ch
ose
n f
or
the
surv
ey.
2.A
sur
vey
dete
rmin
ed t
hat
58%
of
regi
ster
ed v
oter
s in
the
Uni
ted
Sta
tes
supp
ort
incr
ease
dfe
dera
l sp
endi
ng f
or e
duca
tion
.The
mar
gin
of e
rror
for
thi
s su
rvey
is
4%.E
xpla
in i
n yo
urow
n w
ords
wha
t th
is t
ells
you
abo
ut t
he a
ctua
l per
cent
age
of r
egis
tere
d vo
ters
who
sup
port
incr
ease
d sp
endi
ng
for
edu
cati
on.
Sam
ple
an
swer
:Th
ere
is a
95%
ch
ance
th
atth
e ac
tual
per
cen
tag
e o
f vo
ters
su
pp
ort
ing
incr
ease
d f
eder
al s
pen
din
gfo
r ed
uca
tio
n is
bet
wee
n 5
4% a
nd
62%
.
Hel
pin
g Y
ou
Rem
emb
er
3.T
he f
orm
ula
for
mar
gin
of s
ampl
ing
erro
r m
ay b
e tr
icky
to
rem
embe
r.A
goo
d w
ay t
o st
art
is t
o th
ink
abou
t th
e va
riab
les
that
mu
st b
e in
clu
ded
in t
he
form
ula
.Wh
at a
re t
hes
eva
riab
les,
and
wh
at d
o th
ey r
epre
sen
t? W
hat
is
an e
asy
way
to
rem
embe
r w
hic
h v
aria
ble
goes
in
th
e de
nom
inat
or i
n t
he
form
ula
?S
amp
le a
nsw
er:
pis
th
e p
rob
abili
ty o
fa
cert
ain
res
po
nse
an
d n
is t
he
sam
ple
siz
e.T
he
larg
er t
he
sam
ple
siz
e,th
e sm
alle
r th
e m
arg
in o
f er
ror,
so n
mu
st g
o in
th
e d
eno
min
ato
r si
nce
div
idin
g b
y a
larg
er n
um
ber
giv
es a
sm
alle
r n
um
ber
.Th
e sq
uar
e ro
ot
of
asm
alle
r n
um
ber
is a
sm
alle
r n
um
ber
,an
d t
wic
e th
e sq
uar
e ro
ot
of
asm
alle
r n
um
ber
is a
sm
alle
r n
um
ber
.
©G
lenc
oe/M
cGra
w-H
ill75
2G
lenc
oe A
lgeb
ra 2
Sh
apes
of
Dis
trib
uti
on
Cu
rves
Gra
phs
of f
requ
ency
dis
trib
uti
ons
can
be
desc
ribe
d as
eit
her
sym
met
ric
or s
kew
ed.
In a
dis
trib
uti
on s
kew
ed t
o th
e ri
ght,
ther
e ar
e a
larg
er n
um
ber
of h
igh
valu
es.T
he
lon
g “t
ail”
exte
nds
to
the
righ
t.
In a
dis
trib
uti
on s
kew
ed t
o th
e le
ft,t
her
e ar
e a
larg
er n
um
ber
of l
ow v
alu
es.
Th
e “t
ail”
exte
nds
to
the
left
.
For
eac
h o
f th
e fo
llow
ing,
stat
e w
het
her
th
e d
istr
ibu
tion
is
sym
met
ric
or s
kew
ed.I
f it
is
skew
ed,t
ell
wh
eth
er i
t is
sk
ewed
to
the
righ
t or
to
the
left
.
1.2.
3.
sym
met
ric
skew
ed t
o t
he
left
skew
ed t
o t
he
rig
ht
4.5.
6.
sym
met
ric
sym
met
ric
skew
ed t
o t
he
rig
ht
A v
erti
cal
lin
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12-9
12-9
© Glencoe/McGraw-Hill A29 Glencoe Algebra 2
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11. B
C
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A
D
B
C
D
A
An
swer
s
(continued on the next page)
Chapter 12 Assessment Answer Key Form 1 Form 2APage 753 Page 754 Page 755
© Glencoe/McGraw-Hill A30 Glencoe Algebra 2
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:Sample answer:
{7, 9, 18, 20, 24, 40, 50}
A
C
C
A
A
B
D
C
A
D
D
A
B
C
C
D
B
D
A
C
Sample answer: {7, 10, 17, 24, 26, 28, 28}
A
C
C
D
A
B
A
B
C
Chapter 12 Assessment Answer Key Form 2A (continued) Form 2BPage 756 Page 757 Page 758
© Glencoe/McGraw-Hill A31 Glencoe Algebra 2
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B: 74; 4
about 9%
No, the opinions of oneclass may not be typicalof all members of their
age group.
47.5%
normally distributed
10.3�F
106.0�F
Mode; it is thelowest.
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An
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Chapter 12 Assessment Answer Key Form 2CPage 759 Page 760
© Glencoe/McGraw-Hill A32 Glencoe Algebra 2
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B: 77; 3
about 13%
No, library card holdersmay not have opinionsthat are typical of the
community.
47.5%
positively skewed
0.15 in.
0.02
Sample answer: Median; it is
closer to most ofthe values.
630
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60
24
105
Chapter 12 Assessment Answer Key Form 2DPage 761 Page 762
© Glencoe/McGraw-Hill A33 Glencoe Algebra 2
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B: about 1275 students
about 348 people
No, drivers may nothave the same opinion
as nondrivers in thetown.
0.05
�23
2,03328
�
4890
positively skewed
$356.20
126,875.81
Sample answer:Mean; the
Maryland taxesare above the
median but theyare below the
mean.
34,560
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162,162
70; combination; orderdoes not matter.
80,640
7776
An
swer
s
Chapter 12 Assessment Answer Key Form 3Page 763 Page 764
© Glencoe/McGraw-Hill A34 Glencoe Algebra 2
Chapter 12 Assessment Answer KeyPage 765, Open-Ended Assessment
Scoring Rubric
Score General Description Specific Criteria
• Shows thorough understanding of the concepts of solvingproblems involving finding probability, independent anddependent events, permutations, combinations, mutuallyexclusive and inclusive events, statistical measures, andthe normal distribution
• Uses appropriate strategies to solve problems.• Computations are correct.• Written explanations are exemplary.• Goes beyond requirements of some or all problems.
• Shows an understanding of the concepts of solvingproblems involving finding probability, independent anddependent events, permutations, combinations, mutuallyexclusive and inclusive events, statistical measures, andthe normal distribution
• Uses appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are effective.• Satisfies all requirements of problems.
• Shows an understanding of most of the concepts ofsolving problems involving finding probability, independentand dependent events, permutations, combinations,mutually exclusive and inclusive events, statisticalmeasures, and the normal distribution
• May not use appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are satisfactory.• Satisfies the requirements of most of the problems.
• Final computation is correct.• No written explanations or work is shown to substantiate
the final computation.• Satisfies minimal requirements of some of the problems.
• Shows little or no understanding of most of the concepts ofsolving problems involving finding probability, independentand dependent events, permutations, combinations,mutually exclusive and inclusive events, statisticalmeasures, and the normal distribution
• Does not use appropriate strategies to solve problems.• Computations are incorrect.• Written explanations are unsatisfactory.• Does not satisfy the requirements of problems.• No answer may be given.
0 UnsatisfactoryAn incorrect solutionindicating no mathematicalunderstanding of theconcept or task, or nosolution is given
1 Nearly Unsatisfactory A correct solution with nosupporting evidence orexplanation
2 Nearly SatisfactoryA partially correctinterpretation and/orsolution to the problem
3 SatisfactoryA generally correct solution,but may contain minor flawsin reasoning or computation
4 SuperiorA correct solution that is supported by well-developed, accurateexplanations
© Glencoe/McGraw-Hill A35 Glencoe Algebra 2
1a. Student responses must indicate thatAlma’s solution is correct. Explanationsshould indicate that, since A and Brepresent two independent events andthey are looking for the probability thatboth events occurred, the twoprobabilities should be multiplied.Addition would be required if they werelooking for the probability of either oneof the events to occur.
1b. Sample answer for Steven’s solutionP(A) � P(B) � P(A and B) �
�26� � �
36� � �
16� � �
46� � �
23�: A die is rolled.
Find the probability that a numbergreater than 4 or an even number isrolled.
2a. The student response should indicatethat for grades listed, left to right, fromlowest to highest, a negatively skeweddistribution would include a greaternumber of high scores than low scores.Thus, the student should be happy!
2b. Students should explain that the mean,median, and mode of a normaldistribution are the same, so the meancan be presumed to be
�56 �
298
� � 77, or very close to 77. The
fact that there are three standarddeviations between 77 and 98 (orbetween 56 and 77) means that the
standard deviation is �98 �3
77� � 7
�or �77 �3
56� � 7�. Thus, scores in the
range 77 � 7, or between 70 and 84,would earn a grade of C.
3a. Sample answer: For 6 dinner guests,there would be 8 players including Gregand Jacqui, meaning that there wouldbe 70 different ways to arrange theguests in two teams; students shouldindicate that this is a problem involvingcombinations, rather than permutationssince changing the order in whichplayers are selected for each team wouldnot result in the formation of differentteams.
3b. Students should state that this newcondition would, in fact, change thenumber of arrangements. Taking Gregand Jacqui out of the situation for themoment, the question, for the sampleanswer in part a, would become: In howmany ways can you divide a group of 6people into two groups of 3 people each?The number of ways to do so would be C(6, 3) � 20. Then, since there are twoways to place Greg with one group andJacqui with the other, there are only 20 � 2 � 40 possible arrangements ifGreg and Jacqui cannot be on the sameteam.
An
swer
s
Chapter 12 Assessment Answer Key Page 765, Open-Ended Assessment
Sample Answers
In addition to the scoring rubric found on page A34, the following sample answers may be used as guidance in evaluating open-ended assessment items.
© Glencoe/McGraw-Hill A36 Glencoe Algebra 2
1. false; combination
2. true
3. false; standarddeviation
4. false; discreteprobabilitydistributions
5. false; binomialexperiment
6. true
7. true
8. false; compoundevents
9. false; measures ofcentral tendency
10. false; skeweddistribution
11. Sample answer:Mutually exclusiveevents are eventsthat cannot bothhappen at the sametime.
12. A sample is arandom sampleevery possiblesample of that sizehas an equalchance of beingchosen.
1.
2.
3.
4.
5.
Quiz (Lessons 12–4 and 12–5)
Page 767
1.
2.
3.
4.
5.
1.
2.
3.
4.
5.
Quiz (Lessons 12–8 and 12–9)
Page 768
1.
2.
3.
4.
5. about 11%
No, the people surveyedare more likely to prefer
basketball over othersports.
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positively skewed
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combination; 175
5040
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Chapter 12 Assessment Answer Key Vocabulary Test/Review Quiz (Lessons 12–1 through 12–3) Quiz (Lessons 12–6 and 12–7)
Page 766 Page 767 Page 768
© Glencoe/McGraw-Hill A37 Glencoe Algebra 2
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
1.
2.
3.4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15. about 6%
47.5%
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y
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1140
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An
swer
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Chapter 12 Assessment Answer Key Mid-Chapter Test Cumulative ReviewPage 769 Page 770
© Glencoe/McGraw-Hill A38 Glencoe Algebra 2
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11. 12.
13. 14.
15.
16.
17. DCBA
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Chapter 12 Assessment Answer KeyStandardized Test Practice
Page 771 Page 772
© Glencoe/McGraw-Hill A39 Glencoe Algebra 2
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
Sample answer: No;those surveyed aremore likely to listen to a station that airs thetype of music being performed at theconcert.
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0.5%
positively skewed
374.88; 356; no mode; 243.67
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8:5
66
5040
240
Sample answer: n � 2
See students’ answers.
810xy4
1, �3, �11
5, 16, 49, 148, 445
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108
96
63
3072, 2304, 1728, 1296
3200, 2560
7
19, 17, 15
22, 28, 34, 40
Chapter 12 Assessment Answer Key Unit 4 TestPage 773 Page 774
An
swer
s