CHAPTER 9 Core Competencies and Resource Allocation Analyzing Core Competencies
Chapter 9 Resource Masters - MHSchooliv Teacher’s Guide to Using the Chapter 9 Resource Masters...
Transcript of Chapter 9 Resource Masters - MHSchooliv Teacher’s Guide to Using the Chapter 9 Resource Masters...
Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Permission isgranted to reproduce the material contained herein on the condition that suchmaterial be reproduced only for classroom use; be provided to students, teachers,and families without charge; and be used solely in conjunction with GlencoeCalifornia Mathematics, Grade 6. Any other reproduction, for use or sale, isprohibited without prior written permission of the publisher.
Send all inquiries to:Glencoe/McGraw-Hill8787 Orion PlaceColumbus, OH 43240
ISBN: 978-0-07-878304-3MHID: 0-07-878304-6 CAGR6 CRM9
Printed in the United States of America
4 5 6 7 8 9 10 MAL 14 13 12 11 10 09
Consumable Workbooks Many of the worksheets contained in the Chapter Resource Masters
booklets are available as consumable workbooks in both English and Spanish.
MHID ISBNStudy Guide and Intervention Workbook 0-07-878871-4 978-0-07-878871-0
Skills Practice Workbook 0-07-878873-0 978-0-07-878873-4
Practice Workbook 0-07-878875-7 978-0-07-878875-8
Word Problem Practice Workbook 0-07-878877-3 978-0-07-878877-2
Spanish VersionsStudy Guide and Intervention Workbook 0-07-878872-2 978-0-07-878872-7Skills Practice Workbook 0-07-878874-9 978-0-07-878874-1Practice Workbook 0-07-878876-5 978-0-07-878876-5Word Problem Practice Workbook 0-07-878878-1 978-0-07-878878-9
Answers for Workbooks The answers for Chapter 9 of these workbooks can be found in the
back of this Chapter Resource Masters booklet.
StudentWorks Plus™ This CD-ROM includes the entire Student Edition test along with the
English workbooks listed above.
TeacherWorks Plus™ All of the materials found in this booklet are included for viewing,
printing, and editing in this CD-ROM.
Spanish Assessment Masters MHID: 0-07-878879-X ISBN: 978-0-07-878879-6
These masters contain a Spanish version of Chapter 9 Test Form 2A and Form 2C.
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Teacher’s Guide to Using the Chapter 9 Resource Masters .........................................iv
Chapter Resources Chapter 9 Student-Built Glossary ......................1Chapter 9 Family Letter (English) ......................3Chapter 9 Family Activity (English) ....................4Chapter 9 Family Letter (Spanish) .....................5Chapter 9 Family Activity (Spanish)...................6Chapter 9 Anticipation Guide (English)..............7Chapter 9 Anticipation Guide (Spanish) ............8
Lesson 9-1 Simple EventsLesson Reading Guide ......................................9Study Guide and Intervention ..........................10Skills Practice...................................................11Practice ............................................................12Word Problem Practice ....................................13Enrichment .......................................................14
Lesson 9-2 Sample SpacesLesson Reading Guide ....................................15Study Guide and Intervention ..........................16Skills Practice...................................................17Practice ............................................................18Word Problem Practice ....................................19Enrichment .......................................................20
Lesson 9-3 The FundamentalCounting PrincipleLesson Reading Guide ....................................21Study Guide and Intervention ..........................22Skills Practice...................................................23Practice ............................................................24Word Problem Practice ....................................25Enrichment .......................................................26
Lesson 9-4 PermutationsLesson Reading Guide ....................................27Study Guide and Intervention ..........................28Skills Practice...................................................29Practice ............................................................30Word Problem Practice ....................................31Enrichment .......................................................32TI-83/84 Plus Activity .......................................33
Lesson 9-5 CombinationsLesson Reading Guide ....................................34Study Guide and Intervention ..........................35Skills Practice...................................................36Practice ............................................................37Word Problem Practice ....................................38Enrichment .......................................................39TI-83/84 Plus Activity .......................................40
Lesson 9-6 Problem-SolvingInvestigation: Act It OutStudy Guide and Intervention ..........................41Skills Practice...................................................42Practice ............................................................43Word Problem Practice ....................................44
Lesson 9-7 Theoretical andExperimental ProbabilityLesson Reading Guide ....................................45Study Guide and Intervention ..........................46Skills Practice...................................................47Practice ............................................................48Word Problem Practice ....................................49Enrichment .......................................................50TI-83/84 Activity ...............................................51
Lesson 9-8 Compound EventsLesson Reading Guide ....................................52Study Guide and Intervention ..........................53Skills Practice...................................................54Practice ............................................................55Word Problem Practice ....................................56Enrichment .......................................................57TI-73 Activity ....................................................58
Chapter 9 AssessmentStudent Recording Sheet ................................59Rubric for Scoring Pre-AP................................60Chapter 9 Quizzes 1 and 2 ..............................61Chapter 9 Quizzes 3 and 4 ..............................62Chapter 9 Mid-Chapter Test .............................63Chapter 9 Vocabulary Test ...............................64Chapter 9 Test, Form 1 ....................................65Chapter 9 Test, Form 2A..................................67Chapter 9 Test, Form 2B..................................69Chapter 9 Test, Form 2C..................................71Chapter 9 Test, Form 2D..................................73Chapter 9 Test, Form 3 ....................................75Chapter 9 Extended-Response Test ................77Chapter 9 Standardized Test Practice..............78Unit 4 Test ........................................................81
Answers..................................................A1–A37
Contents
iv
Teacher’s Guide to Using the Chapter 9 Resource Masters
The Chapter 9 Resource Masters includes the core materials needed for Chapter 9. Thesematerials include worksheets, extensions, and assessment options. The answers for thesepages appear at the back of this booklet.
All of the materials found in this booklet are included for viewing and printing on theTeacherWorks Plus™ CD-ROM.
Chapter ResourcesStudent-Built Glossary (pages 1–2) Thesemasters are a student study tool thatpresents up to twenty of the key vocabularyterms from the chapter. Students are torecord definitions and/or examples for eachterm. You may suggest that studentshighlight or star the terms with which theyare not familiar. Give this to students beforebeginning Lesson 9-1. Encourage them toadd these pages to their mathematics studynotebooks. Remind them to complete theappropriate words as they study each lesson.
Family Letter and Family Activity(pages 3–6) The letter informs yourstudents’ families of the mathematics theywill be learning in this chapter. The familyactivity helps them to practice problems thatare similar to those on the state test. A fullsolution for each problem is included.Spanish versions of these pages are alsoincluded. Give these to students to takehome before beginning the chapter.
Anticipation Guide (pages 7–8) Thismaster, presented in both English andSpanish, is a survey used before beginningthe chapter to pinpoint what students mayor may not know about the concepts in thechapter. Students will revisit this surveyafter they complete the chapter to see iftheir perceptions have changed.
Lesson ResourcesLesson Reading Guide Get Ready for theLesson reiterates the questions from thebeginning of the Student Edition lesson.Read the Lesson asks students to interpretthe context of and relationships amongterms in the lesson. Finally, RememberWhat You Learned asks students tosummarize what they have learned usingvarious representation techniques. Use as astudy tool for note taking or as an informalreading assignment. It is also a helpful toolfor ELL (English Language Learners).
Study Guide and Intervention Thismaster provides vocabulary, key concepts,additional worked-out examples and CheckYour Progress exercises to use as areteaching activity. It can also be used inconjunction with the Student Edition as aninstructional tool for students who havebeen absent.
Skills Practice This master focuses moreon the computational nature of the lesson.Use as an additional practice option or ashomework for second-day teaching of thelesson.
Practice This master closely follows thetypes of problems found in the Exercisessection of the Student Edition and includesword problems. Use as an additionalpractice option or as homework for second-day teaching of the lesson.
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Word Problem Practice This masterincludes additional practice in solving wordproblems that apply the concepts of thelesson. Use as an additional practice or ashomework for second-day teaching of thelesson.
Enrichment These activities may extendthe concepts of the lesson, offer an historicalor multicultural look at the concepts, orwiden students’ perspectives on themathematics they are learning. They arewritten for use with all levels of students.
Graphing Calculator, ScientificCalculator, or Spreadsheet ActivitiesThese activities present ways in whichtechnology can be used with the concepts insome lessons of this chapter. Use as analternative approach to some concepts or asan integral part of your lesson presentation.
Assessment OptionsThe assessment masters in the Chapter 9Resource Masters offer a wide range ofassessment tools for formative (monitoring)assessment and summative (final) assessment.
Student Recording Sheet This mastercorresponds with the standardized testpractice at the end of the chapter.
Pre-AP Rubric This master providesinformation for teachers and students onhow to assess performance on open-endedquestions.
Quizzes Four free-response quizzes offerassessment at appropriate intervals in thechapter.
Mid-Chapter Test This 1-page testprovides an option to assess the first half ofthe chapter. It parallels the timing of theMid-Chapter Quiz in the Student Editionand includes both multiple-choice and free-response questions.
Vocabulary Test This test is suitable forall students. It includes a list of vocabularywords and 10 questions to assess students’knowledge of those words. This can also beused in conjunction with one of the leveledchapter tests.
Leveled Chapter Tests• Form 1 contains multiple-choice questions
and is intended for use with below gradelevel students.
• Forms 2A and 2B contain multiple-choicequestions aimed at on grade levelstudents. These tests are similar in formatto offer comparable testing situations.
• Forms 2C and 2D contain free-responsequestions aimed at on grade levelstudents. These tests are similar in formatto offer comparable testing situations.
• Form 3 is a free-response test for use withabove grade level students.
All of the above mentioned tests include afree-response Bonus question.
Extended-Response Test Performanceassessment tasks are suitable for allstudents. Sample answers and a scoringrubric are included for evaluation.
Standardized Test Practice These threepages are cumulative in nature. It includesthree parts: multiple-choice questions withbubble-in answer format, griddablequestions with answer grids, and short-answer free-response questions.
Answers• The answers for the Anticipation Guide
and Lesson Resources are provided asreduced pages with answers appearing in red.
• Full-size answer keys are provided for theassessment masters.
Chapter 9 1 Glencoe California Mathematics, Grade 6
Vocabulary TermFound
Definition/Description/Exampleon Page
combination
complementary event
composite event
experimental probability
fair game
Fundamental Counting Principle
independent event
outcome
permutation
NAME ________________________________________ DATE ______________ PERIOD _____
Student-Built Glossary
Ch
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esThis is an alphabetical list of new vocabulary terms you will learn inChapter 9. As you study the chapter, complete each term’s definitionor description. Remember to add the page number where you foundthe term. Add this page to your math study notebook to reviewvocabulary at the end of the chapter.
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Chapter 9 2 Glencoe California Mathematics, Grade 6
Vocabulary TermFound
Definition/Description/Exampleon Page
probability
random
sample space
simple event
theoretical probability
tree diagram
NAME ________________________________________ DATE ______________ PERIOD _____
Student-Built Glossary9C
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Family LetterNAME ________________________________________ DATE ______________ PERIOD _____
Chapter 9 3 Glencoe California Mathematics, Grade 6
Dear Parent or Guardian:
Probability is used in such diverse areas as weather forecasting,
business, and genetics. We use combinations and permutations
to determine the number of possible outcomes in a given
situation. This type of information helps us to decide how to
spend our money or to predict the color of a puppy,s fur.
In Chapter 9, Probability, your child will learn probability, simple
events, sample spaces, the fundamental counting principle,
permutations, combinations, theoretical and experimental
probability, and independent events. Your child will also learn the
problem solving strategy of acting it out. In the study of this
chapter, your child will complete a variety of daily classroom
assignments and activities and possibly produce a chapter project.
By signing this letter and returning it with your child, you agree
to encourage your child by getting involved. Enclosed is an
activity you can do with your child that practices how the math
we will be learning in Chapter 9 might be tested. You may
also wish to log on to ca.gr6math.com for self-check quizzes
and other study help. If you have any questions or comments,
feel free to contact me at school.
Sincerely,
Signature of Parent or Guardian ______________________________________ Date ________
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Family ActivityStandards Practice
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 9 4 Glencoe California Mathematics, Grade 6
1. Joshua is playing a game with hisfriends. The object of the game is to geta sum of 9 when two standard numbercubes are rolled.
How many possible ways are there forrolling two number cubes? How many ofthese ways have a sum of 9?
A 36 ways; 4 with a sum of 9B 36 ways; 8 with a sum of 9C 16 ways; 4 with a sum of 9D 16 ways; 8 with a sum of 9
Fold here.
Solution1. Since there are 6 possible outcomes for
each number cube, there are 6 � 6 or 36 possible rolls.
In order for the sum of the numbercubes to be 9, we can have the followingcombinations:
There are 4 possible combinations thatwill result in a sum of 9.
The answer is A.
2. Justine is designing a probabilityexperiment in which she can simulatefinding the probability of getting snowovernight if the weatherman said thatthere is a 25% chance that theprecipitation overnight will be rain, a50% chance that the precipitation willbe snow, and a 25% chance that therewill be no precipitation at all.
Which of the following would bestsimulate what might happen overnight?A toss a coinB spin a spinner with four equal
sectionsC roll a standard number cubeD pick from 25 marbles in a bag
Solution2. Hint: Consider the number of outcomes
possible and consider their probabilitiesas fractions of a whole.
The probabilities can all be expressed in
terms of �14
�. Choice B is the only option
that represents fourths.
The answer is B.
9
Fold the page along the dashed line. Work each problem on another piece of paper.Then unfold the page to check your work.
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Carta a la familiaNOMBRE ______________________________________ FECHA ____________ PERÍODO ___
Capítulo 9 5 Glencoe California Mathematics, Grade 6
Estimado padre o apoderado:
La probabilidad se usa en áreas tan diversas como el pronóstico
del tiempo, los negocios y la genética. Usamos combinaciones y
permutaciones para determinar el número de posibles resultados
en una situación dada. Este tipo de información nos ayuda a
decidir cómo gastar nuestro dinero o predecir el color del pelaje
de un cachorro.
En el Capítulo 9, Probabilidad, su hijo(a) aprenderá sobre
probabilidad, eventos simples, espacios muestrales, el principio fun-
damental de conteo, permutaciones, combinaciones, probabilidad
teórica y experimental y eventos independientes. Su hijo(a) tam-
bién aprenderá la estrategia de solución de problemas mediante
simulacros. En el estudio de este capítulo, su hijo(a) completará
una variedad de tareas y actividades diarias y es posible que tra-
baje en un proyecto del capítulo.
Al firmar esta carta y devolverla con su hijo(a), usted se com-
promete a ayudarlo(a) a participar en su aprendizaje. Junto con
esta carta, va incluida una actividad que puede realizar con
él(ella) y la cual practica lo que podrían encontrar en las prue-
bas de los conceptos matemáticos que aprenderán en el
Capítulo 9. Además, visiten ca.gr6math.com para ver
autocontroles y otras ayudas para el estudio. Si tiene cualquier
pregunta o comentario, por favor contácteme en la escuela.
Cordialmente,
Firma del padre o apoderado ________________________________________ Fecha ______
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Actividad en familiaPráctica de estándares
NOMBRE ______________________________________ FECHA ____________ PERÍODO ___
Capítulo 9 6 Glencoe California Mathematics, Grade 6
1. Joshua está jugando con sus amigos. Elobjeto del juego es obtener una suma de9 al lanzar dos cubos numeradosestándares.
¿Cuántas maneras posibles hay delanzar dos cubos numerados? ¿Cuántasde éstas suman 9?
A 36 maneras; 4 suman 9B 36 maneras; 8 suman 9C 16 maneras; 4 suman 9D 16 maneras; 8 suman 9
Doblen aquí.
Solución1. Puesto que existen 6 resultados posibles
para cada cubo numerado, hay 6 � 6 ó 36 tiros posibles.
Para lograr que la suma de los cubosnumerados sea 9, se tienen lascombinaciones siguientes:
Hay 4 combinaciones posibles queresultarán en una suma de 9.
La respuesta es A.
2. Justine diseña un experimento deprobabilidades en donde puede simularla búsqueda de la probabilidad de quenieve durante la noche, si el meteoró-logo dijo que hay un 25% de probabili-dad de que la precipitación sea lluvia,un 50% de que la precipitación seanieve y un 25% de que no ocurraprecipitación alguna.
¿Cuál de los siguientes simularía mejorlo que puede ocurrir durante la noche?A lanzar una moneda al aireB girar un girador de cuatro secciones
igualesC lanzar un cubo numerado estándarD escoger de entre 25 canicas en una
bolsa
Solución2. Ayuda: Consideren el número de
resultados posibles y consideren susprobabilidades como fracciones de untodo.
Las probabilidades pueden expresarse en
términos de �14
�. La opción B es la única
que representa cuartos.
La respuesta es B.
Cubo 1 Cubo 23 66 34 55 4
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1
9
Doblen la página a lo largo de las líneas punteadas. Resuelvan cada problema en otra hoja de papel. Luego, desdoblen la página y revisen las respuestas.
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NAME ________________________________________ DATE ______________ PERIOD _____
Anticipation GuideProbability
Chapter 9 7 Glencoe California Mathematics, Grade 6
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Before you begin Chapter 9
• Read each statement.
• Decide whether you Agree (A) or Disagree (D) with the statement.
• Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure).
After you complete Chapter 9
• Reread each statement and complete the last column by entering an A or a D.
• Did any of your opinions about the statements change from the first column?
• For those statements that you mark with a D, use a piece of paper to write an example of why you disagree.
Step 2
Step 1
STEP 1 Statement STEP 2A, D, or NS A or D
1. The probability of an event happening is a ratio that compares the number of favorable outcomes to the number of unfavorable outcomes.
2. If the probability of an event happening is �35
� then it is more likely for the event to happen than to not happen.
3. In a probability experiment, a tree diagram can be used to show all the possible outcomes.
4. The Fundamental Counting Principle states that the number of possible outcomes can also be found by division.
5. To find the value of 4!, add 4 � 3 � 2 � 1.
6. In a combination, choosing event A then event B would be the same as choosing event B then event A.
7. The experimental probability of an event happening will always be close to the theoretical probability of that event happening.
8. The act it out strategy is a good way to solve problems because the results will be the same every time the experiment is repeated.
9. A compound event consists of two or more simple events.10. The probability of two independent events is found the same
way as the probability of two dependent events.
NOMBRE ______________________________________ FECHA ____________ PERÍODO ___
Ejercicios preparatoriosProbabilidad
Capítulo 9 8 Glencoe California Mathematics, Grade 6
Copyright ©
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9
PASO 2
Antes de comenzar el Capítulo 9
• Lee cada enunciado.
• Decide si estás de acuerdo (A) o en desacuerdo (D) con el enunciado.
• Escribe A o D en la primera columna O si no estás seguro(a) de la respuesta,escribe NS (No estoy seguro(a).
Después de completar el Capítulo 9
• Vuelve a leer cada enunciado y completa la última columna con una A o una D.
• ¿Cambió cualquiera de tus opiniones sobre los enunciados de la primera columna?
• En una hoja de papel aparte, escribe un ejemplo de por qué estás en desacuerdo con losenunciados que marcaste con una D.
PASO 1
PASO 1 PASO 2A, D o NS
EnunciadoA o D
1. La probabilidad de que ocurra un evento es una razón que compara el número de resultados favorables con el número de resultados desfavorables.
2. Si la probabilidad de que ocurra un evento es �35
�, entonces es más probable que ocurra el evento a que no ocurra.
3. En un experimento de probabilidad, se puede usar undiagrama de árbol para mostrar todos los resultados posibles.
4. El principio fundamental de contar establece que el número po-sible de resultados puede también calcularse mediante división.
5. Para calcular el valor de 4!, suma 4 � 3 � 2 � 1.
6. En una combinación, escoger el evento A y después el evento B sería igual a escoger el evento B y después el evento A.
7. La probabilidad experimental de que ocurra un evento siempre será cercana a la probabilidad teórica de que ocurra dicho evento.
8. La estrategia de hacer un simulacro es una buena forma de resolver problemas porque los resultados serán los mismos cada vez que se repita el experimento.
9. Un evento compuesto consta de dos o más eventos simples.10. La probabilidad de dos eventos independientes se encuentra
de la misma manera que la probabilidad de dos eventos dependientes.
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Less
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Chapter 9 9 Glencoe California Mathematics, Grade 6
Get Ready for the LessonRead the introduction at the top of page 460 in your textbook. Writeyour answers below.
1. What fraction of the taffy is vanilla? Write in simplest form.
2. Suppose you take one piece of taffy from the box without looking. Areyour chances of picking vanilla the same as picking root beer? Explain.
Read the LessonUse the information from the introduction to answer Exercises 3–5.
3. How do you read P(cherry)?
4. P(cherry) � �468�
; where does the 6 come from? Where does the 48 come
from?
5. Probability can be written as a fraction, a decimal, or a percent. WriteP(cherry) as a decimal.
6. If there is a 25% chance that something will happen, what is the chancethat it will not happen? What are these two events called?
Remember What You Learned7. Write the equation P(A) � P(not A) � 1 in words. What does it mean with
respect to event A?
NAME ________________________________________ DATE ______________ PERIOD _____
Lesson Reading GuideSimple Events
9-1 6SDAP3.3
Exercises
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionSimple Events
Chapter 9 10 Glencoe California Mathematics, Grade 6
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9-1
What is the probability of rolling a multiple of 3 on a number cubemarked with 1, 2, 3, 4, 5, and 6 on its faces.
P(multiple of 3) �
� �26� Two numbers are multiples of 3: 3 and 6.
� �13� Simplify.
The probability of rolling a multiple of 3 is �13� or about 33.3%.
What is the probability of not rolling a multiple of 3 on a numbercube marked with 1, 2, 3, 4, 5, and 6 on its faces?
P(A) � P(not A) � 1
�13� � P(not A) � 1 Substitute �
13
� for P(A).
��13� ��
13� Subtract �
13
� from each side��������
P(not A) � �23� Simplify.
The probability of not rolling a multiple of 3 is �23� or about 66.7%.
A set of 30 cards is numbered 1, 2, 3, …, 30. Suppose you pick a card atrandom without looking. Find the probability of each event. Write asa fraction in simplest form.
1. P(12) 2. P(2 or 3)
3. P(odd number) 4. P(a multiple of 5)
5. P(not a multiple of 5) 6. P(less than or equal to 10)
multiples of 3 possible���total numbers possible
The probability of a simple event is a ratio that compares the number of favorable outcomes to thenumber of possible outcomes. Outcomes occur at random if each outcome occurs by chance.
Two events that are the only ones that can possibly happen are complementary events. The sum ofthe probabilities of complementary events is 1.
Example 1
Example 2
6SDAP3.3
NAME ________________________________________ DATE ______________ PERIOD _____
Skills PracticeSimple Events
Chapter 9 11 Glencoe California Mathematics, Grade 6
Less
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A set of 12 cards is numbered 1, 2, 3, …12. Suppose you pick a card atrandom without looking. Find the probability of each event. Write asa fraction in simplest form.
1. P(5) 2. P(6 or 8)
3. P(a multiple of 3) 4. P(an even number)
5. P(a multiple of 4) 6. P(less than or equal to 8)
7. P(a factor of 12) 8. P(not a multiple of 4)
9. P(1, 3, or 11) 10. P(a multiple of 5)
The students at Job’s high schoolwere surveyed to determine theirfavorite foods. The results areshown in the table at the right.Suppose students were randomlyselected and asked what theirfavorite food is. Find the probabilityof each event. Write as a fraction insimplest form.
11. P(steak) 12. P(spaghetti)
13. P(cereal or seafood) 14. P(not chow mein)
15. P(pizza) 16. P(cereal or steak)
17. P(not steak) 18. P(not cereal or seafood)
19. P(chicken) 20. P(chow mein or spaghetti)
Favorite Food Responsespizza 19steak 8chow mein 5seafood 4spaghetti 3cereal 1
6SDAP3.3
A set of cards is numbered 1, 2, 3, … 24. Suppose you pick a card atrandom without looking. Find the probability of each event. Write asa fraction in simplest form.
1. P(5) 2. P(multiple of 4) 3. P(6 or 17)
4. P(not equal to 15) 5. P(not a factor of 6) 6. P(odd number)
COMMUNITY SERVICE The table shows the students involved incommunity service. Suppose one student is randomly selected torepresent the school at a state-wide awards ceremony. Find theprobability of each event. Write as a fraction in simplest form.
7. P(boy) 8. P(not 6th grader)
9. P(girl) 10. P(8th grader)
11. P(boy or girl) 12. P(6th or 7th grader)
13. P(7th grader) 14. P(not a 9th grader)
MENU A delicatessen serves different menu items, of which 2 aresoups, 6 are sandwiches, and 4 are salads. How likely is it for eachevent to happen if you choose one item at random from the menu?Explain your reasoning.
15. P(sandwich) 16. P(not a soup) 17. P(salad)
18. NUMBER CUBE What is the probability of rolling an even number or a prime number on a number cube? Write as a fraction in simplest form.
19. CLOSING TIME At a convenience store there is a 25% chance a customerenters the store within one minute of closing time. Describe thecomplementary event and find its probability.
NAME ________________________________________ DATE ______________ PERIOD _____
PracticeSimple Events
Chapter 9 12 Glencoe California Mathematics, Grade 6
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Community Servicegirls 15boys 256th graders 207th graders 88th graders 12
6SDAP3.3
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Word Problem PracticeSimple Events
Chapter 9 13 Glencoe California Mathematics, Grade 6
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COINS Susan opened her piggy bank and countedthe number of each coin. The table at the rightshows the results. For Exercises 1–3, assume thatthe coins are put in a bag and one is chosen atrandom.
1. What is the probability that a quarteris chosen?
2. What is the probability that a nickel ora dime is chosen?
3. What is the probability that the chosencoin is worth more than 5 cents?
4. NUMBER CUBES Juan has two numbercubes, each with faces numbered 1, 2, …6. What is the probability thathe can roll the cubes so that the sum ofthe faces showing equals 11?
5. SKATEBOARDS Carlotta bought a newskateboard for which the probability ofhaving a defective wheel is 0.015. Whatis the probability of not having adefective wheel?
6. CALCULATORS Jake’s teacher had 6calculators for 28 students to use. If thefirst students to use the calculators arechosen at random, what is theprobability that Jake will get one?
7. VEHICLES The rental car company had14 sedans and 8 minivans available torent. If the next customer picks avehicle at random, what is theprobability that a minivan is chosen?
8. MUSIC Tina has 16 pop CDs,6 classical, and 2 rock. Tina chooses aCD at random. What is the probabilityshe does not choose a classical CD?
Coin Numberquarters 15
dimes 21
nickels 22
pennies 32
6SDAP3.3
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
Chapter 9 14 Glencoe California Mathematics, Grade 6
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Coin-Tossing ExperimentsIf a coin is tossed 3 times, there are 8 possible outcomes. They are listed in thetable below.
Once all the outcomes are known, the probability of any event can be found.For example, the probability of getting 2 heads is �
38�. Notice that this is the
same as getting 1 tail.
1. A coin is tossed 4 times. Complete this chart to show the possibleoutcomes.
2. What is the probability of getting all tails?
3. Now complete this table. Make charts like the one in Exercise 1 to helpfind the answers. Look for patterns in the numbers.
4. What happens to the number of outcomes? the probability of all tails?
Number of Heads 0 1 2 3
Outcomes TTT HTT HHT HHH
THT THH
TTH HTH
Number of Heads 0 1 2 3
Outcomes TTTT
4
Number of Coin Tosses 2 3 4 5 6 7 8
Total Outcomes
Probability of Getting AllTails
6SDAP3.1
NAME ________________________________________ DATE ______________ PERIOD _____
Lesson Reading Guide Sample Spaces
Chapter 9 15 Glencoe California Mathematics, Grade 6
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Get Ready for the LessonComplete the Mini Lab at the top of page 465 in your textbook. Writeyour answers below.
1. Before you play, make a conjecture. Do you think that each player has anequal chance of winning? Explain.
2. Now, play the game. Who won? What was the final score?
Read the Lesson3. How does a tree diagram resemble a tree?
4. How can you use a table to find the number of possible outcomes of anevent?
5. How do you know the game played in Example 3 is fair?
Remember What You Learned6. Draw a tree diagram that shows a fair game that is different from
the examples in your textbook. Can you think of a way to draw a tree diagram that shows a game that is not fair? Make sure you include a description if the game is not clear from your diagram.
6SDAP3.1
Exercises
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionSample Spaces
Chapter 9 16 Glencoe California Mathematics, Grade 6
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WATCHES A certain type of watch comes in brown or black and in asmall or large size. Find the number of color-size combinations thatare possible.
Make a table to show the sample space. Then give the total number of outcomes.
There are four different color and size combinations.
CHILDREN The chance of having either a boy or a girl is 50%. What is the probability of the Smiths having two girls?
Make a tree diagram to show the sample space. Then find the probability of having two girls.
The sample space contains 4 possible outcomes. Only 1 outcome has both children beinggirls. So, the probability of having two girls is �
14�.
For each situation, make a tree diagram or table to show the samplespace. Then give the total number of outcomes.
1. choosing an outfit from a green shirt, blue shirt, or a red shirt, and blackpants or blue pants
2. choosing a vowel from the word COUNTING and a consonant from theword PRIME
boyboy
girl boy, girl
Child 1 Child 2 Sample Space
girlboy
girl
girl, boy
boy, boy
girl, girl
A game in which players of equal skill have an equal chance of winning is a fair game. A tree diagram or table is used to show all of the possible outcomes, or sample space, in a probabilityexperiment.
Color Size
Brown Small
Brown Large
Black Small
Black Large
Example 1
Example 2
6SDAP3.1
NAME ________________________________________ DATE ______________ PERIOD _____
Skills PracticeSample Spaces
Chapter 9 17 Glencoe California Mathematics, Grade 6
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The spinner at the right is spun twice.
1. Draw a tree diagram to represent the situation.
2. What is the probability of getting at least one A?
For each situation, make a tree diagram or table to show thesample space. Then give the total number of outcomes.
3. choosing a hamburger or hot dog and potato salad or macaronisalad
4. choosing a vowel from the word COMPUTER and a consonant from the word BOOK
5. choosing between the numbers 1, 2 or 3, and the colors blue, red, or green
B
C A
6SDAP3.1
For each situation, find the sample space using a table or treediagram.
1. choosing blue, green, or yellow wall paint with white, beige, or graycurtains
2. choosing a lunch consisting of a soup,salad, and sandwich from the menu shown in the table.
3. GAME Kimiko and Miko are playing a game in which each girl rolls anumber cube. If the sum of the numbers is a prime number, then Mikowins. Otherwise Kimiko wins. Find the sample space. Then determinewhether the game is fair.
NAME ________________________________________ DATE ______________ PERIOD _____
PracticeSample Spaces
Chapter 9 18 Glencoe California Mathematics, Grade 6
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Soup Salad SandwichTortellini Caesar Roast Beef
Lentil Macaroni HamTurkey
blue
blue paint, white curtains
blue paint, beige curtains
blue paint, gray curtains
white
beige
gray
green paint, white curtains
green paint, beige curtains
green paint, gray curtains
white
beige
gray
yellow paint, white curtains
yellow paint, beige curtains
yellow paint, gray curtains
white
beige
gray
green
yellow
Paint Sample SpaceCurtains
6SDAP3.1
NAME ________________________________________ DATE ______________ PERIOD _____
Word Problem Practice Sample Spaces
Chapter 9 19 Glencoe California Mathematics, Grade 6
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1. GASOLINE Craig stops at a gas stationto fill his gas tank. He must choosebetween full-service or self-service andbetween regular, midgrade, andpremium gasoline. Draw a treediagram or table showing the possiblecombinations of service and gasolinetype. How many possible combinationsare there?
3. COINS In Exercise 2, what is theprobability of getting 2 heads, then 2 tails?
4. EQUIPMENT The computer accessorythat Joanne is considering selling ather store comes in white, beige, gray,or black and as an optical mouse,mechanical mouse, or trackball. Howmany combinations of color and modelmust she stock in order to have at leastone of every possible combination?
2. COINS Judy tosses a coin 4 times. Drawa tree diagram or table showing thepossible outcomes. What is theprobability of getting at least 2 tails?
6SDAP3.1
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
Chapter 9 20 Glencoe California Mathematics, Grade 6
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Probabilities and RegionsThe spinner at the right can be used to indicate that the probability of landing in either of two regions is �
12�.
P(A) � �12� P(B) � �
12�
Read the description of each spinner. Using a protractor and ruler,divide each spinner into regions that show the indicated probability.
1. Two regions A and B: the probability of landing in region A is �34�.
What is the probability of landing in region B?
2. Three regions A, B, and C: the probability of landing in region A
is �12� and the probability of landing in region B is �
14�. What is the
probability of landing in region C?
3. Three regions A, B, and C: the probability of landing in region A
is �38� and the probability of landing in region B is �
18�. What is the
probability of landing in region C?
4. Four regions A, B, C, and D: the probability of landing in region A
is �116�
, the probability of landing in region B is �18�, and the probability
of landing in region C is �14�. What is the probability of landing in
region D?
5. The spinner at the right is an equilateral triangle, divided into regions by line segments that divide the sides in half. Is the spinner divided into regions of equal probability?
A
B
6SDAP3.1
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 9 21 Glencoe California Mathematics, Grade 6
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Get Ready for the LessonRead the introduction at the top of page 471 in your textbook. Writeyour answers below.
1. According to the table, how many sizes of juniors’ jeans are there?
2. How many lengths are there?
3. Find the product of the two numbers you found in Exercises 1 and 2.
4. Draw a tree diagram to help you find the number of different size and length combinations. How does the number of outcomes compare to the product you found above?
Read the Lesson5. What operation is used in the Fundamental
Counting Principle?
6. How is the information in a tree diagram or table different from the information provided by counting?
Remember What You Learned7. Write the Fundamental Counting Principle in your own words.
6SDAP3.1Lesson Reading GuideThe Fundamental Counting Principle
Exercises
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 9 22 Glencoe California Mathematics, Grade 6
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CLOTHING Andy has 5 shirts, 3 pairs of pants, and 6 pairs of socks.How many different outfits can Andy choose with a shirt, pair ofpants, and pair of socks?
Andy can choose 90 different outfits.
Use the Fundamental Counting Principle to find the total number ofoutcomes in each situation.
1. rolling two number cubes
2. tossing 3 coins
3. picking one consonant and one vowel
4. choosing one of 3 processor speeds, 2 sizes of memory, and 4 sizes of hard drive
5. choosing a 4-, 6-, or 8-cylinder engine and 2- or 4-wheel drive
6. rolling 2 number cubes and tossing 2 coins
7. choosing a color from 4 colors and a number from 4 to 10
If event M can occur in m ways and is followed by event N that can occur in n ways, then the event Mfollowed by N can occur in m � n ways. This is called the Fundamental Counting Principle.
number of shirts number of pants number of socks total number of outfits� � � �
5 � 3 � 6 � 90
Example 1
6SDAP3.1Study Guide and InterventionThe Fundamental Counting Principle
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 9 23 Glencoe California Mathematics, Grade 6
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Use the Fundamental Counting Principle to find the total number ofoutcomes in each situation.
1. rolling two number cubes and tossing one coin
2. choosing rye or Bermuda grass and 3 different mixtures of fertilizer
3. making a sandwich with ham, turkey, or roast beef; Swiss or provolonecheese; and mustard or mayonaise
4. tossing 4 coins
5. choosing from 3 sizes of distilled, filtered, or spring water
6. choosing from 3 flavors of juice and 3 sizes
7. choosing from 35 flavors of ice cream; one, two, or three scoops; and sugaror waffle cone
8. picking a day of the week and a date in the month of April
9. rolling 3 number cubes and tossing 2 coins
10. choosing a 4-letter password using only vowels
11. choosing a bicycle with or without shock absorbers; with or withoutlights; and 5 color choices
12. a license plate that has 3 numbers from 0 to 9 and 2 letters
6SDAP3.1Skills Practice The Fundamental Counting Principle
Use the Fundamental Counting Principle to find the total number ofoutcomes in each situation.
1. choosing from 8 car models, 5 exterior paint colors, and 2 interior colors
2. selecting a year in the last decade and a month of the year
3. picking from 3 theme parks and 1-day, 2-day, 3-day, and 5-day passes
4. choosing a meat and cheese sandwich from the list shown in the table
5. tossing a coin and rolling 2 number cubes
6. selecting coffee in regular or decaf, with or without cream, and with orwithout sweeteners
7 COINS Find the number of possible outcomes if 2 quarters, 4 dimes, and 1nickel are tossed.
8. SOCIAL SECURITY Find the number of possible 9-digit social securitynumbers if the digits may be repeated.
9. AIRPORTS Jolon will be staying with his grandparents for a week. Thereare four flights that leave the airport near Jolon's home that connect toan airport that has two different flights to his grandparents’ hometown.Find the number of possible flights. Then find the probability of takingthe earliest flight from each airport if the flight is selected at random.
10. ANALYZE TABLES The table shows the kinds of homes offered by a residential builder. If the builder offers a discount on one home at random, find the probability it will be a 4-bedroom home with an open porch. Explain your reasoning.
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 9 24 Glencoe California Mathematics, Grade 6
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Number of Style of Type ofBedrooms Kitchen Porch5-bedroom Mediterranean Open4-bedroom Contemporary Screen3-bedroom Southwestern
Colonial
Cheese MeatProvolone SalamiSwiss TurkeyAmerican TunaCheddar Ham
6SDAP3.1PracticeThe Fundamental Counting Principle
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 9 25 Glencoe California Mathematics, Grade 6
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1. SURFBOARD Jay owns 3 surfboards and2 wetsuits. If he takes one surfboardand one wetsuit to the beach, howmany different combinations can hechoose?
2. SHOPPING John is trying to decidewhich bag of dog food to buy. The brandhe wants comes in 4 flavors and 3 sizes.How many choices are there?
3. LOTTERY To purchase a lottery ticket,you must select 4 numbers from 0 to 9.How many possible lottery tickets canbe chosen?
4. RESTAURANTS Miriam’s favoriterestaurant has 3 specials every day.Each special has 2 choices of vegetableand 3 choices of dessert. How manydifferent meals could Miriam have?
5. ROUTES When Sunil goes to thebuilding where he works, he can gothrough 4 different doors into the lobby.Then he can go to the seventh floor bytaking 2 different elevators or 2different stairways. How manydifferent ways can Sunil get fromoutside the building to the seventhfloor?
6. STEREOS Jailin went to her local stereostore. Given her budget and theavailable selection, she can choosebetween 2 CD players, 5 amplifiers,and 3 pairs of speakers. How manydifferent stereos can Jailin purchase?
7. DESSERT For dessert you can chooseapple, cherry, blueberry, or peach pie toeat, and milk or juice to drink. Howmany different combinations can youchoose from?
8. TESTS John is taking a true or falsequiz. There are six questions on thequiz. How many ways can the quiz beanswered?
6SDAP3.1Word Problem PracticeThe Fundamental Counting Principle
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
Chapter 9 26 Glencoe California Mathematics, Grade 6
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9-3
Curious CubesIf a six-faced cube is rolled any number of times, the theoretical probability ofthe cube landing on any given face is �
16�.
Each cube below has six faces and has been rolled 100 times. Theoutcomes have been tallied and recorded in a frequency table. Basedon the data in each frequency table, what can you say are probablyon the unseen faces of each cube?
1.
2.
3.
4.
5.
14
5
14
5
Blue Red
Red
Yellow Blue
Red
14
5 Outcome Tally1 152 143 184 165 196 18
Outcome Tallyblue 17
red 30
yellow 53
Outcome Tallyred 30
blue 16
blank 54
Outcome Tally
1 34
4 32
5 34
Outcome Tally1 145 134 182 16
blank 39
6SDAP3.1
NAME ________________________________________ DATE ______________ PERIOD _____
Lesson Reading GuidePermutations
Chapter 9 27 Glencoe California Mathematics, Grade 6
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Get Ready for the LessonComplete the Mini Lab at the top of page 475 in your textbook. Writeyour answers below.
1. When you first started to make your list, how many choices did you havefor your first class?
2. Once your first class was selected, how many choices did you have for thesecond class? Then, the third class?
Read the Lesson3. Explain why the arrangement Science, Math, Language Arts is a
permutation of Math, Science, Language Arts.
4. In Example 1 on page 475, why is there only 1 choice for the third class?
5. In Example 2 on page 476, why are there only 7 choices for second place?
Remember What You Learned6. Look up the word permute in a dictionary. How does the meaning of this
word relate to the concepts in this lesson, especially the concept ofpermutations?
6SDAP3.1
Exercises
Example 2
Example 3
Example 1
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionPermutations
Chapter 9 28 Glencoe California Mathematics, Grade 6
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Find the value of 5 � 4 � 3 � 2 � 1.
5 � 4 � 3 � 2 � 1� 120 Simplify.
Find the value of 4 � 3 � 2 � 1 � 2 � 1.
4 � 3 � 2 � 1 � 2 � 1� 48 Simplify.
BOOKS How many ways can 4 different books be arranged on abookshelf?
This is a permutation. Suppose the books are placed on the shelf from left to right.There are 4 choices for the first book.
There are 3 choices that remain for the second book.There are 2 choices that remain for the third book.
There is 1 choice that remains for the fourth book.
4 � 3 � 2 � 1� 24 Simplify.
So, there are 24 ways to arrange 4 different books on a bookshelf.
Find the value of each expression.
1. 3 · 2 · 1 2. 7 · 6 · 5 · 4 · 3 · 2 · 1
3. 6 · 5 · 4 · 3 · 2 · 1 · 3 · 2 · 1 4. 9 · 8 · 7
5. How many ways can you arrange the letters in the word GROUP?
6. How many different 4-digit numbers can be created if no digit can berepeated? Remember, a number cannot begin with 0.
A permutation is an arrangement, or listing, of objects in which order is important. You can use theFundamental Counting Principle to find the number of possible arrangements.
6SDAP3.1
NAME ________________________________________ DATE ______________ PERIOD _____
Skills PracticePermutations
Chapter 9 29 Glencoe California Mathematics, Grade 6
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Find the value of each expression.
1. 2 · 1 2. 4 · 3 · 2 · 1
3. 3 · 2 · 1 · 5 · 4 · 3 · 2 · 1 4. 9 · 8 · 7 · 6 · 5 · 4 · 3 · 2 · 1
5. 2 · 1 · 8 · 7 · 6 · 5 · 4 · 3 · 2 · 1 6. 3 · 2 · 1 · 2 · 1
7. 11 · 10 · 9 8. 10 · 9 · 8 · 7 · 6 · 5 · 4 · 3 · 2 · 1
9. 5 · 4 · 3 · 2 · 1 · 2 · 1 10. 5 · 4 · 3 · 2
11. 8 · 7 · 6 · 5 · 4 · 3 · 2 · 1 12. 6 · 5 · 4 · 3 · 2 · 1
13. How many ways can you arrange the letters in the word PRIME?
14. How many ways can you arrange 8 different crates on a shelf if they areplaced from left to right?
6SDAP3.1
Solve each problem.
1. NUMBERS How many different 2-digit numbers can be formed from thedigits 4, 6, and 8? Assume no number can be used more than once.
2. LETTERS How many permutations are possible of the letters in the wordNUMBERS?
3. PASSENGERS There are 5 passengers in a car. In how many ways can thepassengers sit in the 5 passenger seats of the car?
4. PAINTINGS Mr. Bernstein owns 14 paintings, but has only enough wallspace in his home to display three of them at any one time: one in thehallway, one in the den, and one in the parlor. How many ways can Mr.Bernstein display three paintings in his home?
5. DOG SHOW Mateo is one of the six dog owners in the terrier category. Ifthe owners are selected in a random order to show their dogs, how manyways can the owners show their dogs?
6. TIME Michel, Jonathan, and two of their friends each ride their bikes to school. If they have an equally-likely chance of arriving first, what isthe probability that Jonathan will arrive first and Michel will arrivesecond?
7. BIRTHDAY Glen received 6 birthday cards. If he is equally likely to readthe cards in any order, what is the probability he reads the card from hisparents and the card from his sister before the other cards?
CODES For Exercises 8–10, use the following information. A bank giveseach new customer a 4-digit code number which allows the newcustomer to create their own password. The code number is assignedrandomly from the digits 1, 3, 5, and 7, and no digit is repeated.
8. What is the probability that the code number for a new customer willbegin or end with a 7?
9. What is the probability that the code number will not contain a 5?
10. What is the probability that the code number will start with 371?
NAME ________________________________________ DATE ______________ PERIOD _____
PracticePermutations
Chapter 9 30 Glencoe California Mathematics, Grade 6
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NAME ________________________________________ DATE ______________ PERIOD _____
Word Problem PracticePermutations
Chapter 9 31 Glencoe California Mathematics, Grade 6
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1. AREA CODES How many different 3-digit area codes can be created if nodigit can be repeated?
2. CARDS Jason is dealt five playingcards. In how many different orderscould Jason have been dealt the samehand?
3. PASSWORDS How many different 3-letter passwords are possible if noletter may be repeated?
4. RACING All 22 students in Amy’s classare going to run the 100-meter dash. Inhow many ways can the students finishin first, second, and third place?
5. LETTERS How many ways can youarrange the letters in the wordHISTORY?
6. PARKING The parking lot for a companyhas three parking spaces for compactcars. The company has 8 employeeswith compact cars. How many ways canthe compact parking spaces be filled?
7. SERIAL NUMBERS How many different 6-digit serial numbers are available ifno digit can be repeated?
8. WINNERS There are 156 ways for 2 carsto win first and second place in a race.How many cars are in the race?
6SDAP3.1
Cyclic Permutations1. George, Alan, and William are in the same math class. George has five
different shirts and wears a different one each day. In how many wayscan George wear his five shirts in five days?
2. Alan has three different shirts and William has four. Which of the threestudents, George, Alan, or William, goes the greatest number of daysbefore he has to wear a shirt for the second time? Explain.
George, Alan, and William always wear their shirts in the same order.Suppose that George’s 5 shirts are red, tan, green, black, and white. He wears his shirts following this pattern:
B W R T G B W R T …
No matter where George is in the pattern, his friends can always figure outwhich shirt George will wear next. Since these permutations are the samewhen they make up part of a cycle, they are called cyclic permutations.
3. Alan has shirts that are white, black, and purple. Make an organized listof all the different permutations.
4. How many different ways are there for Alan to wear his shirts so that hisfriends recognize different patterns? Explain.
5. William has athletic shirts that are labeled 1, 2, 3, and 4. Make anorganized list of all the different permutations.
6. How many different ways are there for William to wear his shirts so that hisfriends recognize different patterns? Explain.
7. CHALLENGE For any given number of shirts, how can you determine thenumber of ways a person could wear the shirts to produce uniquepatterns?
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
Chapter 9 32 Glencoe California Mathematics, Grade 6
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Exercises
Example 1
NAME ________________________________________ DATE ______________ PERIOD _____
TI-83/84 Plus ActivityPermutations
Chapter 9 33 Glencoe California Mathematics, Grade 6
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You can use a graphing calculator to help you find the number of permutations.
25 people are auditioning for 5 different parts in a play. In how many ways can the 5 parts be assigned?
To calculate a permutation, find the total number ofobjects (n) and the number taken at one time (r). In thisproblem, n � 25. Because 5 students are needed, r � 5.
Enter: 25 2 5 6,375,600
The parts can be assigned in 6,375,600 different ways.
Find the value of each permutation for the given values of n and r.
1. n � 5, r � 2 2. n � 8, r � 3 3. n � 9, r � 6
4. n � 6, r � 2 5. n � 10, r � 6 6. n � 12, r � 4
7. n � 20, r � 2 8. n � 15, r � 7 9. n � 18, r � 3
Solve.
10. Employees of Spies, Inc., are given 3-digit code numbers made up ofthe digits 1, 3, 5, 7, and 9. How many different 3-digit code numberscan be created?
11. How many different 4-letter arrangements are there in the letters A, S,N, D, T, R, and Y?
12. Twenty students have entered an art contest. Five students will eachreceive different awards. How many different groups of 5 studentscould be selected to receive awards?
ENTERMATH
NAME ________________________________________ DATE ______________ PERIOD _____
Lesson Reading GuideCombinations
Chapter 9 34 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
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-Hill, a division of T
he McG
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panies, Inc.
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Get Ready for the LessonRead the introduction at the top of page 480 in your textbook. Writeyour answers below.
1. Use the first letter of each name to list all of the permutations of co-captains. How many are there?
2. Cross out any arrangement that contains the same letters as another onein the list. How many are there now?
3. Explain the difference between the two lists above.
Read the Lesson4. How can you find the number of combinations of objects in a set?
5. Why might it be easier to calculate the number of combinations of a set ofobjects using a permutation rather than making a list?
For Exercises 6 and 7, refer to Example 2 on page 525 in your textbook.
6. In the diagram, how many points are there? How many line segmentsconnect to any one point?
7. How does your answer to Exercise 6 above correspond to Example 2 inyour book?
Remember What You Learned8. Work with a partner. Take turns thinking of situations in which a
selection from a group must be made, where order is or is not important.Tell each other which situations are permutations and which arecombinations. Solve each problem and show your work.
6SDAP3.1
Exercises
Jill was asked by her teacher to choose 3 topics from the 8 topics given to her. How many different three-topic groups could she choose?
There are 8 · 7 · 6 permutations of three-topic groups chosen from eight. There are 3 · 2 · 1ways to arrange the groups.
�8 �7 � 6
� � �3366
� � 56
So, there are 56 different three-topic groups.
Tell whether each situation represents a permutation or combination.Then solve the problem.
On a quiz, you are allowed to answer any 4 out of the 6 questions.How many ways can you choose the questions?
This is a combination because the order of the 4 questions is not important. So, there are 6 · 5 · 4 · 3 permutations of four questions chosen from six. There are 4 · 3 · 2 · 1 orders inwhich these questions can be chosen.
�6 � 5
4�!4 � 3� � �
32640
� � 15
So, there are 15 ways to choose the questions.
Five different cars enter a parking lot with only 3 empty spaces.How many ways can these spaces be filled?
This is a permutation because each arrangement of the same 3 cars counts as a distinctarrrangement. So, there are 5 · 4 · 3 or 60 ways the spaces can be filled.
Tell whether each situation represents a permutation or combination.Then solve the problem.
1. How many ways can 4 people be chosen from a group of 11?
2. How many ways can 3 people sit in 4 chairs?
3. How many ways can 2 goldfish be chosen from a tank containing 15 goldfish?
Example 2
Example 3
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionCombinations
Chapter 9 35 Glencoe California Mathematics, Grade 6
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An arrangement, or listing, of objects in which order is not important is called a combination. You canfind the number of combinations of objects by dividing the number of permutations of the entire set bythe number of ways each smaller set can be arranged.
Example 1
6SDAP3.1
3 � 2 � 1
4 � 3 � 2 � 1
NAME ________________________________________ DATE ______________ PERIOD _____
Skills PracticeCombinations
Chapter 9 36 Glencoe California Mathematics, Grade 6
Copyright ©
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Tell whether each situation represents a permutation or combination.Then solve the problem.
1. You are allowed to omit two out of 12 questions on a quiz. How manyways can you select the questions to omit?
2. Six students are to be chosen from a class of 18 to represent the class at amath contest. How many ways can the six students be chosen?
3. How many different 5-digit zip codes are possible if no digits arerepeated?
4. In a race with six runners, how many ways can the runners finish first,second, or third?
5. How many ways can two names be chosen from 76 in a raffle if only oneentry per person is allowed?
6. How many ways can six students be arranged in a lunch line?
7. A family has a bike rack that fits seven bikes but they only have fivebikes. How many ways can the bikes fit in the bike rack?
8. How many ways can you select three sheriff deputies from eightcandidates?
9. How many ways can four finalists be selected from 50 contestants?
10. How many 4-digit pin numbers are available if no number is repeated?
11. How many handshakes can occur between five people if everyone shakeshands?
6SDAP3.1
Solve each problem.
1. BASKETBALL In how many ways can a coach select 5 players from a teamof 10 players?
2. BOOKS In how many ways can 3 books be selected from a shelf of 25books?
3. CAFETERIA In how many ways can you choose 2 side dishes from 15items?
4. CHORES Of 8 household chores, in how many ways can you do three-fourths of them?
5. ELDERLY Latanya volunteers to bake and deliver pastries to elderly peoplein her neighborhood. In how many different ways can Latanya deliver to2 of the 6 elderly people in her neighborhood?
6. DELI A deli makes potato, macaroni, three bean, Caesar, 7-layer, andGreek salads. The deli randomly makes only four salads each day. What isthe probability that the four salads made one day are 7-layer, macaroni,Greek, and potato?
7. AUTOGRAPHS A sports memorabilia enthusiast collected autographed baseballs from the players in the table. The enthusiast is giving one autographed baseball to each of his three grandchildren. If the baseballs are selected at random, what is the probability that the Hank Aaron, Alex Rodriquez,and Mickey Mantle autographed baseballs are given to his grandchildren?
For Exercises 8–10, tell whether each problem represents apermutation or a combination. Then solve the problem.
8. LOCKS In how many ways can three different numbers be selected from10 numbers to open a keypad lock?
9. MOVIES How many ways can 10 DVDs be placed on a shelf?
10. TRANSPORTATION Eight people need transportation to the concert. Howmany different groups of 6 people can ride with Mrs. Johnson?
NAME ________________________________________ DATE ______________ PERIOD _____
PracticeCombinations
Chapter 9 37 Glencoe California Mathematics, Grade 6
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PlayerCal RipkinHank AaronBarry BondsAlex RodriquezMickey Mantle
6SDAP3.1
NAME ________________________________________ DATE ______________ PERIOD _____
Word Problem Practice Combinations
Chapter 9 38 Glencoe California Mathematics, Grade 6
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1. SNACKS A vending machine can displaysix snacks. If there are eight differentkinds of snacks available, how manydifferent groups of six different snackscan be displayed?
2. MUSIC Each month, Jose purchases twoCDs from a selection of 20 bestsellingCDs. How many different pairs of CDscan Jose choose if he chooses twodifferent CDs?
3. TESTS On a math test, you can chooseany 20 out of 23 questions. How manydifferent groups of 20 questions canyou choose?
4. RESTAURANTS The dinner special at alocal pizza parlor gives you the choiceof two toppings from a selection of sixtoppings. How many different choicesare possible if two different toppingsare chosen?
5. TESTING In a science fair experiment,two units are selected for testing fromevery 500 units produced. How manyways can these two units be selected?
6. MEETINGS Linda’s teacher divided theclass into groups of five and requiredeach member of a group to meet withevery other member of that group. Howmany meetings will each group have?
7. BASEBALL A baseball coach has 13players to fill nine positions. How manydifferent teams could he put together?
8. GEOMETRY Ten points are marked on acircle. How many different trianglescan be drawn between any threepoints?
6SDAP3.1
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
Chapter 9 39 Glencoe California Mathematics, Grade 6
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From Impossible to Certain EventsA probability is often expressed as a fraction. As you know, an event that isimpossible is given a probability of 0 and an event that is certain is given aprobability of 1. Events that are neither impossible nor certain are given aprobability somewhere between 0 and 1. The probability line below showsrelative probabilities.
Determine the probability of an event by considering its place on thediagram above.
1. Medical research will find a cure for all diseases.
2. There will be a personal computer in each home by the year 2010.
3. One day, people will live in space or under the sea.
4. Wildlife will disappear as Earth’s human population increases.
5. There will be a fifty-first state in the United States.
6. The sun will rise tomorrow morning.
7. Most electricity will be generated by nuclear power by the year 2010.
8. The fuel efficiency of automobiles will increase as the supply of gasolinedecreases.
9. Astronauts will land on Mars.
10. The percent of high school students who graduate and enter college willincrease.
11. Global warming problems will be solved.
12. All people in the United States will exercise regularly within the nearfuture.
equally likelyprettylikely
1
certainnot solikely
14
12
34
0
impossible
6SDAP3.1
Exercises
NAME ________________________________________ DATE ______________ PERIOD _____
TI-83/84 Plus ActivityCombinations
Chapter 9 40 Glencoe California Mathematics, Grade 6
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A graphing calculator can be used to solve problems involving combinations. On the TI-83/84Plus, the combination function can be found in the MATH (PRB) menu.
How many ways can 2 people be chosen from a group of 10 people?
Since order does not matter, this is a combination.
Enter: 10 3 2 45
So, the number of ways 2 people can be chosen from a group of 10 people is 45.
How many 5-card hands can be chosen from a deck of 52 cards?
Since order does not matter, this is a combination.
Enter: 52 3 5 2,598,960
So, the number of 5-card hands that can be chosen from a 52-card deck is2,598,960.
Solve each problem.
1. How many groups of 3 people can be chosen from a group of 5 people?
2. How many groups of 4 people can be chosen from a group of 8 people?
3. How many groups of 10 people can be chosen from a group of 20 people?
4. How many groups of 2 people can be chosen from a group of 12 people?
5. How many groups of 8 people can be chosen from a group of 9 people?
6. How many 2-topping pizzas can be made from a pizza restaurant offering 6 different toppings?
7. How many 3-topping pizzas can be made from a pizza restaurant offering 10 different toppings?
8. How many 7-card hands can be chosen from a deck of 52 cards?
9. How many 4-card hands can be chosen from a deck of 52 cards?
10. How many two-topping sundaes can be made from an ice cream shop offering 9 different toppings?
ENTERMATH
ENTERMATH
Example 1
Example 2
Exercises
Example
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 9 41 Glencoe California Mathematics, Grade 6
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CLOTHING Ricardo has two shirts and three pairs of pants to chosefrom for his outfit to wear on the first day of school. How manydifferent outfits can he make by wearing one shirt and one pair ofpants?
By acting out a problem, you are able to see all possible solutions to the problem being posed.
Explore We know that he has two shirts and three pairs of pants to choose from. We canuse a coin for the shirts and an equally divided spinner labeled for the pants.
Plan Let’s make a list showing all possible outcomes of tossing a coin and thenspinning a spinner.
Solve H � HeadsT � TailsSpinner � 1, 2, 3
There are six possible outcomes of flipping a coin and spinning a spinner.So, there are 6 different possible outfits that Ricardo can wear for the first dayof school.
Check Flipping a coin has two outcomes and there are two shirts. Spinning a three-section spinner has three outcomes and there are three pairs of pants.Therefore, the solution of 6 different outcomes with a coin and spinnerrepresent the 6 possible outfit outcomes for Ricardo.
Flip a Coin Spin a SpinnerH 1H 2H 3T 1T 2T 3
1. SCIENCE FAIR There are 4 students with projects to present at the schoolscience fair. How many different ways can these 4 projects be displayedon four tables in a row?
2. GENDER Determine whether flipping a coin is a good way to predict thegender of the next 5 babies born at General Hospital. Justify youranswer.
3. OLYMPICS Four runners are entered in the first hurdles heat of twelveheats at the Olympics. The first two move on to the next round.Assuming no ties, how many different ways can the four runners come infirst and second place?
6SDAP3.2, 6SDAP2.4Study Guide and InterventionProblem-Solving Investigation: Act It Out
Use the act it out strategy to solve.
1. SCHOOL Determine whether rolling a 6-sided number cube is a good wayto answer a 20-question multiple-choice test if there are six choices foreach question. Justify your answer.
2. GYMNASTICS Five gymnasts are entered in a competition. Assuming thatthere are no ties, how many ways can first, second, and third places beawarded?
3. LUNCH How many ways can 3 friends sit together in three seats at lunch?
4. SCHEDULE How many different schedules can Sheila create if she has totake English, math, science, social studies, and art next semester. Assumethat there is only one lunch period available.
5. BAND CONCERTS The band is having a holiday concert. In the first row,the first trumpet is always furthest to the right and the first trombone isalways the furthest to the left. How many ways are there to arrange theother 4 people who need to sit in the front?
6. TEAMS Mr. D is picking teams for volleyball in gym by having thestudents count off by 2’s. The 1’s will be on one team and the 2’s on theother. Would flipping a coin would work just as well to pick the teams?Justify your answer.
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 9 42 Glencoe California Mathematics, Grade 6
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he McG
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9-6 6SDAP3.2, 6SDAP2.4Skills PracticeProblem-Solving Investigation: Act it Out
Select the Operation
Mixed Problem Solving
For Exercises 1 and 2, use the act it outstrategy.
1. POP QUIZ Use the information in thetable to determine whether tossing anickel and a dime is a good way toanswer a 5-question multiple-choicequiz if each question has answer choicesA, B, C, and D. Justify your answer.
2. BOWLING Bill, Lucas, Carmen, andDena go bowling every week. Whenordered from highest to lowest, howmany ways can their scores be arrangedif Lucas is never first and Carmenalways beats Bill?
Use any strategy to solve Exercises 3and 4. Some strategies are shown below.
3. BOOKS What is the probability of fivebooks being placed in alphabetical orderof their titles if randomly put on a bookshelf?
4. NUMBER THEORY The sum of a 2-digitnumber and the 2-digit number whenthe digits are reversed is 77. If thedifference of the same two numbers is45, what are the two 2-digit numbers?
For Exercises 5 and 6, select theappropriate operation(s) to solve theproblems. Justify your solution(s) andsolve the problem.
5. BASEBALL In one game, Rafael was up tobat 3 times and made 2 hits. In anothergame, he was up to bat 5 times with nohits. What percent of the times at batdid Rafael make a hit?
6. RESTAURANT A restaurant offers thepossibility of 168 three-course dinners.Each dinner has an appetizer, an entrée,and a dessert. If the number ofappetizers decreases from 7 to 5, findhow many fewer possible three-coursedinners the restaurant offers.
NAME ________________________________________ DATE ______________ PERIOD _____
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PROBLEM-SOLVING STRATEGIES
• Use the four-step plan.
• Draw a diagram.
• Determine reasonable answers.
• Act it out.
Nickel Dime Answer ChoiceH H AH T BT H CT T D
6SDAP3.2, 6SDAP2.4PracticeProblem-Solving Investigation: Act It Out
Solve each problem using any strategy you have learned.
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 9 44 Glencoe California Mathematics, Grade 6
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3. BASEBALL Thirty-two teams are playingin the championship. If a team iseliminated once it loses, how manytotal games will be played in thechampionship?
4. GEOMETRY Find the next two terms inthe sequence.
5. POOL RENTAL The table below showshow much Ford Middle School wascharged to rent the pool for a partybased on the number of hours it wasrented. Predict the cost for 5 hours.
6. GEOMETRY Use the formula D � rtwhere D is the distance, r is the rate,and t is the time to determine how farAlyssa drove if she drove 55 miles perhour for 4 hours.
7. SCHOOL ELECTIONS How many ways can a president, vice president,secretary and treasurer be elected from a choice of 6 students?
8. SHOPPING Morty bought skis. The skiscost $215 and he got $35 in change.How much did Morty pay with?
# of hours Cost1 $1201.5 $1802 $2402.5 $300
1. POLLS Out of 200 people, 32% said thattheir favorite animal was a cat and44% said that their favorite animal wasa dog. How many more people chosedog than cat?
2. PEACHES Roi is picking peaches He
needs a total of 3�12
� bushels of peaches.
If he has already picked 3 bushels, howmany more does he need to pick?
A 2 bushels C 3�12
� bushels
B �12
� bushel D 3 bushels
6SDAP3.2, 6SDAP2.4Word Problem PracticeProblem-Solving Investigation: Act It Out
Get Ready for the LessonComplete the Mini Lab at the top of page 486 in your textbook. Writeyour answers below.
1. Compare the number of times you expected to roll a sum of 7 with thenumber of times you actually rolled a sum of 7. Then compare your resultto the results of other groups.
2. Write the probability of rolling a sum of 7 out of 36 rolls using thenumber of times you expected to roll a 7 from Step 1. Then write theprobability of rolling a sum of 7 out of 36 rolls using the number of timesyou actually rolled a sum of 7 from Step 2.
Read the Lesson3. Look up the word experimental in a dictionary. Write the meaning for the
word as used in the lesson.
4. How does theoretical probability differ from experimental probability?
5. Complete the sentence: Experimental probability can be based onand can be used to make predictions about future
events.
Remember What You Learned6. Work with a partner. Design an experiment that you can use to express
the experimental probability of an event. Compare your findings withthose of others in your class.
NAME ________________________________________ DATE ______________ PERIOD _____
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6SDAP3.2Lesson Reading Guide Theoretical and Experimental Probability
Exercises
The graph shows the results of an experiment in which a number
cube was rolled 100 times. Find the experimentalprobability of rolling a 3 for this experiment.
P(3) �
� �11060�
or �245�
The experimental probability of rolling a 3 is �245�
, which is close to its theoretical
probabilityof �16�.
In a telephone poll, 225 people were asked for whom they planned to vote in the race
for mayor. What is the experimental probability of Juarez being elected?
Of the 225 people polled, 75 planned to vote for Juarez.
So, the experimental probability is �27255�
or �13�.
Suppose 5,700 people vote in the election.How many can be expected to vote for Juarez?
�13� � 5,700 � 1,900
About 1,900 will vote for Juarez.
For Exercises 1–3, use the graph of a survey of 150 students asked whether they prefer cats or dogs.
1. What is the probability of a student preferring dogs?
2. Suppose 100 students were surveyed. How many can be expected to prefer dogs?
3. Suppose 300 students were surveyed. How many can be expected to prefer cats? DogsCats
60
80
100
40
0
20
120
140
Num
ber o
f Stu
dent
s
18
132
number of times 3 occurs����number of possible outcomes
6321
20
10
15
25
0
5Num
ber o
f Rol
ls
54
14 1316
1921
17
Number Showing
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 9 46 Glencoe California Mathematics, Grade 6
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Experimental probability is found using frequencies obtained in an experiment or game. Theoreticalprobability is the expected probability of an event occurring.
CandidateNumber of
PeopleJuarez 75Davis 67Abramson 83
Example 1
Example 2
Example 3
6SDAP3.2Study Guide and InterventionTheoretical and Experimental Probability
For Exercises 1–5, a number cube is rolled 50 times and the resultsare shown in the graph below.
1. Find the experimental probability of rolling a 2.
2. What is the theoretical probability of rolling a 2?
3. Find the experimental probability of not rolling a 2.
4. What is the theoretical probability of not rolling a 2?
5. Find the experimental probability of rolling a 1.
For Exercises 6–9, use the results of the survey at the right.
6. What is the probability that a person’s favorite season is fall? Write the probability as a fraction.
7. Out of 300 people, how many would you expect to say that fall is their favorite season?
8. Out of 20 people, how many would you expect to say that they like all theseasons?
9. Out of 650 people, how many more would you expect to say that they likesummer than say that they like winter?
Spring
Summer
Fall
Winter
None, I likethem all
13%
39%
25%
13%
10%
What is your favoriteseason of the year?
6321
8
10
12
4
6
14
0
2
Num
ber o
f Rol
ls
54
108
6
9
5
12
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 9 47 Glencoe California Mathematics, Grade 6
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Theoretical and Experimental Probability
For Exercises 1–4, a number cube is rolled 24 times and lands on 2four times and on 6 three times.
1. Find the experimental probability of landing on a 2.
2. Find the experimental probability of not landing on a 6.
3. Compare the experimental probability you found in Exercise 1 to itstheoretical probability.
4. Compare the experimental probability you found in Exercise 2 to itstheoretical probability.
ENTERTAINMENT For Exercises 5–7, use the results of the survey in the table shown.
5. What is the probability that someonein the survey considered readingbooks or surfing the Internet as thebest entertainment value? Write theprobability as a fraction.
6. Out of 500 people surveyed, how manywould you expect considered readingbooks or surfing the Internet as thebest entertainment value?
7. Out of 300 people surveyed, is itreasonable to expect that 30considered watching television as thebest entertainment value? Why or whynot?
For Exercises 8–10, a spinner marked with four sections blue, green,yellow, and red was spun 100 times. The results are shown in the table.
8. Find the experimental probability of landing on green.
9. Find the experimental probability of landing on red.
10. If the spinner is spun 50 more times,how many of these times would you expect the pointer to land on blue?
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 9 48 Glencoe California Mathematics, Grade 6
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Section FrequencyBlue 14
Green 10Yellow 8
Red 68
Best Entertainment ValueType of Entertainment PercentPlaying Interactive Games 48%Reading Books 22%Renting Movies 10%Going to Movie Theaters 10%Surfing the Internet 9%Watching Television 1%
6SDAP3.2PracticeTheoretical and Experimental Probability
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 9 49 Glencoe California Mathematics, Grade 6
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HOBBIES For Exercises 1–3, use the WINTER ACTIVITIES For Exercises 5 and 6,graph of a survey of 24 seventh grade use the graph of a survey with 104students asked to name their favorite responses in which respondents were hobby . asked about their favorite winter
activities.
10 20 30 40 50 60 700
Building a snowmanSnowboarding/skiing
Sledding
What is your favorite winter activity?
1469
21
Respondents
2 4 6 8 10 12 140
SingingHanging with friends
Building thingsBike riding
T.V.Computer
Roller skatingSports
What is your favorite hobby?
13
12
333
8
Number of Students
1. What is the probability that a student’sfavorite hobby is roller skating?
2. Suppose 200 seventh grade studentswere surveyed. How many can beexpected to say that roller skating istheir favorite hobby?
3. Suppose 60 seventh grade studentswere surveyed. How many can beexpected to say that bike riding is theirfavorite hobby?
4. MARBLES A bag contains 5 blue, 4 red,9 white, and 6 green marbles. If amarble is drawn at random andreplaced 100 times, how many timeswould you expect to draw a greenmarble?
5. What is the probability that someone’sfavorite winter activity is building asnowman? Write the probability as afraction.
6. If 500 people had responded, how manywould have been expected to listsledding as their favorite winteractivity? Round to the nearest wholeperson.
6SDAP3.2Word Problem PracticeTheoretical and Experimental Probability
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
Chapter 9 50 Glencoe California Mathematics, Grade 6
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Rolling a DodecahedronA dodecahedron is a solid. It has twelve faces, and each face is a pentagon.
At the right, you see a dodecahedron whose faces are marked with the integers from 1 through 12. You can roll this dodecahedron just as you roll a number cube. With the dodecahedron, however, there are twelve equally likely outcomes.
Refer to the dodecahedron shown at the right. Find the probability of each event.
1. P(5) 2. P(odd)
3. P(prime) 4. P(divisible by 5)
5. P(less than 4) 6. P(fraction)
You can make your own dodecahedron by cutting out the pattern at the right. Fold along each of the solid lines. Then use tape to join the faces together so that your dodecahedron looks like the one shown above.
7. Roll your dodecahedron 100 times. Record your results on a separate sheet of paper, using a table like this.
8. Use your results from Exercise 7. Find the experimental probability for each of the events described in Exercises 1–6.
Outcome
1
2
Tally Frequency
1 2
3
45
6
7
11
128
9
10
2
11 10
1
36
6SDAP3.2
Exercises
NAME ________________________________________ DATE ______________ PERIOD _____
TI-73 ActivityExperimental Probability
Chapter 9 51 Glencoe California Mathematics, Grade 6
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Use your calculator to simulate flipping a coin or rolling a number cube. These features arefound in the MATH PRB (probability) menu. The calculator displays a random number thatrepresents heads or tails on a coin or the number on a number cube. The calculator callsnumber cubes dice.
Roll two number cubes 100 times. Calculate the experimental probability ofrolling double-1, double-2, double-3, double-4, double-5, or double-6.
Step 1 Clear Home. Step 2 Choose the dice feature in MATH PRB.
[MEM] 5 7
Step 3 The display shows dice( . Use 2 dice. Step 4 Interpret the result and continue for
2 100 rolls.
The display shows an ordered pair of digits, like (3 5). This means the first cube shows a 3 and thesecond cube shows a 5. If a double, like (2 2) or (5 5), appears, tally it in the chart below. Continue with the next roll by pressing .
Use your graphing calculator to complete the following.
1. Complete the table for 100 rolls. Calculate the Fraction and Percentcolumns.
2. The theoretical probability ofrolling double-1 (or any otherdouble) is 1/36 or about 3%.Compare this theoreticalprobability with yourexperimental results.
3. Do another experiment, but use the coin feature of MATH PRB. Explore the probability of afamily with three children having all girls. Flip 3 coins. Each coin stands for one child. If theresult is a 1, then the child is a boy; if it is 0, then the child is a girl. Flip the three coins 100 times. Tally the results of 3 girls and of 3 boys. Describe your results.
ENTER
ENTER
MATHENTER2nd
Double Tally Number Fraction Percent
(1, 1)
(2, 2)
(3, 3)
(4, 4)
(5, 5)
(6, 6)
Tally Number Fraction Percent
All girls (0, 0, 0)
All boys (1, 1, 1)
Example 1
NAME ________________________________________ DATE ______________ PERIOD _____
Lesson Reading GuideCompound Events
Chapter 9 52 Glencoe California Mathematics, Grade 6
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Get Ready for the LessonRead the introduction at the top of page 492 in your textbook. Writeyour answers below.
1. What is the probability of Omar being in the second heat? in Lane 3?
2. Multiply your answers in Exercises 1. What does this number represent?
Read the LessonUse the introduction to the lesson to answer Exercises 4–6.
3. What does a compound event consist of?
4. Define independent events.
5. Write the probability of independent events in symbols.
6. How can you find the probability of two independent events?
Remember What You Learned7. List several independent compound events. Explain why you consider the
events to be independent.
6SDAP3.4, 6SDAP3.5
Exercises
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionCompound Events
Chapter 9 53 Glencoe California Mathematics, Grade 6
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A coin is tossed and a number cube is rolled. Find the probabilityof tossing tails and rolling a 5.
P(tails) � �12� P(5) � �
16�
P(tails and 5) � �12� � �
16� or �1
12�
So, the probability of tossing tails and rolling a 5 is �112�
.
MARBLES A bag contains 7 blue, 3 green, and 3 red marbles. If Agnes randomly draws two marbles from the bag, replacing the first
before drawing the second, what is the probability of drawing a green and then ablue marble?
P(green) � 3/131 13 marbles, 3 are green
P(blue) � 7/13 13 marbles, 7 are blue
P(green, then blue) � �133�
· �172�
� �12619
�
So, the probability that Agnes will draw a green, then a blue marble is �12619
�.
1. Find the probability of rolling a 2 and then an even number on twoconsecutive rolls of a number cube.
2. A penny and a dime are tossed. What is the probability that the pennylands on heads and the dime lands on tails?
3. Lazlo’s sock drawer contains 8 blue and 5 black socks. If he randomlypulls out one sock, what is the probability that he picks a blue sock?
A compound event consists of two or more simple events. If the outcome of one event does not affectthe outcome of a second event, the events are called independent events. The probability of twoindependent events can be found by multiplying the probability of the first event by the probability ofthe second event.
Example 1
Example 2
6SDAP3.4, 6SDAP3.5
NAME ________________________________________ DATE ______________ PERIOD _____
Skills PracticeCompound Events
Chapter 9 54 Glencoe California Mathematics, Grade 6
Copyright ©
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9-8
1. Four coins are tossed. What is the probability of tossing all heads?
2. One letter is randomly selected from the word PRIME and one letter israndomly selected from the word MATH. What is the probability thatboth letters selected are vowels?
3. A card is chosen at random from a deck of 52 cards. It is then replacedand a second card is chosen. What is the probability of getting a jack andthen an eight?
For Exercises 4–6, use the information below.
A standard deck of playing cards contains 52 cards in four suits of 13 cardseach. Two suits are red and two suits are black. Find each probability. Assumethe first card is replaced before the second card is drawn.
4. P(black, queen) 5. P(black, diamond) 6. P(jack, queen)
7. What is the probability of spinning a number greater than 5 on a spinnernumbered 1 to 8 and tossing a tail on a coin?
8. Two cards are chosen at random from a standard deck of cards withreplacement. What is the probability of getting 2 aces?
9. A CD rack has 8 classical CDs, 5 pop CDs, and 3 rock CDs. One CD ischosen and replaced, then a second CD is chosen. What is the probabilityof choosing a rock CD then a classical CD?
10. A jar holds 15 red pencils and 10 blue pencils. What is the probability ofdrawing one red pencil from the jar?
6SDAP3.4, 6SDAP3.5
A number cube is rolled and a spinner like the one shown is spun. Find each probability.
1. P(6 and D) 2. P(multiple of 2 and B) 3. P(not 6 and not A)
A set of 7 cards is labeled 1–7. A second set of 12 cards contains the followingcolors: 3 green, 6 red, 2 blue, and 1 white. One card from each set is selected. Findeach probability.
4. P(6 and green) 5. P(prime and blue) 6. P(odd and red)
7. P(7 and white) 8. P(multiple of 3 and red) 9. P(even and white)
A coin is tossed, a number cube is rolled, and a letter is picked fromthe word framer.
10. P(tails, 5, m) 11. P(heads, odd, r) 12. P(heads, 6, vowel)
13. P(tails, prime, consonant) 14. P(not tails, multiple of 3, a) 15. P(not heads, 2, f )
16. TOLL ROAD Mr. Espinoza randomly chooses one of five toll booths whenentering a toll road when driving to work. What is the probability he willselect the middle toll booth on Monday and Tuesday?
MARBLES For Exercises 17–20, use theinformation in the table shown to find eachprobability. After a marble is randomly pickedfrom a bag containing marbles of four differentcolors, the color of the marble is observed andthen it is returned to the bag.
17. P(red) 18. P(green, blue)
19. P(red, white, blue) 20. P(blue, blue, blue)
A
D
CB
NAME ________________________________________ DATE ______________ PERIOD _____
PracticeCompound Events
Chapter 9 55 Glencoe California Mathematics, Grade 6
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MarblesColor NumberWhite 6Green 2Red 1Blue 3
6SDAP3.4, 6SDAP3.5
NAME ________________________________________ DATE ______________ PERIOD _____
Word Problem Practice Compound Events
Chapter 9 56 Glencoe California Mathematics, Grade 6
Copyright ©
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9-8
1. SAFETY Eighty percent of all Californiadrivers wear seat belts. If three driversare pulled over, what is the probabilitythat all would be wearing their seatbelts? Write as a percent to the nearesttenth.
2. VEGETABLES A nationwide surveyshowed that 65% of all children in theUnited States dislike eating vegetables.If three children are chosen at random,what is the probability that all threedislike eating vegetables? Write as apercent to the nearest tenth.
3. QUALITY In a shipment of 50calculators, 4 are defective. Onecalculator is randomly selected andtested. What is the probability that it isdefective?
4. MARBLES A bag contains 6 greenmarbles, 2 blue marbles, and 3 whitemarbles. Gwen draws one marble fromthe jar and replaces it. Jeff then drawsone marble from the jar. What is theprobability that Gwen draws a bluemarble and Jeff draws a white marble?
5. DEMONSTRATION Ms. Morris needs astudent to help her with ademonstration for her class of 12 girlsand 14 boys. She randomly chooses astudent. What is the probability thatshe chooses a girl?
6. SURVEY Ruben surveyed his class andfound that 4 out of 22 students walk toschool. If one of the 22 students isselected at random, what is theprobability that the chosen studentDOES NOT walk to school?
6SDAP3.4, 6SDAP3.5
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
Chapter 9 57 Glencoe California Mathematics, Grade 6
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Compound EventsThe game of roulette is played by dropping a ballinto a spinning, bowl-shaped wheel. When thewheel stops spinning, the ball will come to rest inany of 38 locations.
On a roulette wheel, the eighteen even numbersfrom 2 through 36 are colored red and theeighteen odd numbers from 1 through 35 arecolored black. The numbers 0 and 00 are coloredgreen.
To find the probability of two independent events,the results of two spins, find the probability ofeach event first.
P(red) � �1388�
or �199�
P(black) � �1388�
or �199�
Then multiply.
P(red, then black) � �199�
� �199�
or �38611�
Find each probability.
1. black, then black
2. prime number, then a composite number
3. a number containing at least one 0, then a number containing at leastone 2
4. red, then black
5. the numbers representing your age, month of birth, and then day of birth
0 3 9 15 20 3226
410
1621
3327
5
1117223428006122335
2918
713
124
3036
8
214 19 31 25
6SDAP3.4, 6SDAP3.5
NAME ________________________________________ DATE ______________ PERIOD _____
TI-73 ActivityProbability and Percents
Chapter 9 58 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
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he McG
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panies, Inc.
9-8
When you solve probability problems, use your calculator to express fractions as decimalsand percents.
Two number cubes are rolled. Find the probability that both cubes show anodd number. Report the probability as a percent.
The probability of a cube showing an odd number is �12�. To find the probabilitythat both first and second cubes are odd, multiply �12� by �12�.
Keys: 1 2 1 2 Display: �21� * �2
1� �4
1�
�41� .25
100 Ans*100 25
The probability that both cubes show odd numbers is 25%.
There are 3 red marbles and 5 blue marbles in a bag. Two marbles are drawnand the first marble is replaced before the second is drawn.What is theprobability of drawing 2 blue marbles? Report the probability as a percent.
Keys: Display:
5 8 5 8 �85
�*�85
� �625
4�
Display: �625
4� 0.390625100 Display:Ans*100 0.390625
The probability of drawing 2 blue marbles is 39.06%.
Find each probability. Report your answer as a percent. Round percents to thenearest hundredth when necessary.
1. You draw 2 marbles from a bag replacing the first marble before drawing the second. The bagcontains 4 yellow marbles, 2 white marbles, and 6 red marbles.
a. What is the probability that your first marble is red and the second is yellow?
b. What is the probability that both marbles are white?
c. What is the probability that neither marble is red?
d. What is the probability that both marbles are red?
2. You have three number cubes.
a. What is the probability that you will roll all even numbers?
b. What is the probability that you will roll only numbers less than 3?
c. CHALLENGE What is the probability that you will roll a 1 on only one number cube?
ENTER
ENTERF D
ENTERbcbc
ENTER
ENTERF D
ENTERbcbc
F D←←
F D←←
Example 1
Example 2
NAME ________________________________________ DATE ______________ PERIOD _____
Student Recording SheetUse this recording sheet with pages 504–505 of the Student Edition.
Chapter 9 59 Glencoe California Mathematics, Grade 6
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Read each question. Then fill in thecorrect answer.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Record your answers for Question 12 onthe back of this paper.
A B C D
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
Pre-AP
Ass
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NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Chapter 9 60 Glencoe California Mathematics, Grade 6
9 Rubric for Scoring Pre-AP(Use to score the Pre-AP question on page 505 of the Student Edition.)
General Scoring Guidelines• If a student gives only a correct numerical answer to a problem but does not show how he or she
arrived at the answer, the student will be awarded only 1 credit. All extended response questionsrequire the student to show work.
• A fully correct answer for a multiple-part question requires correct responses for all parts of thequestion. For example, if a question has three parts, the correct response to one or two parts of thequestion that required work to be shown is not considered a fully correct response.
• Students who use trial and error to solve a problem must show their method. Merely showing thatthe answer checks or is correct is not considered a complete response for full credit.
Exercise 12 Rubric
Score Specific Criteria4 A correct tree diagram is given. The propability that Paula will hear a country song
first on Friday night is correctly determined to be �15
�. The probability that Paula
will hear a rap song first on Friday night and a jazz song first on Saturday night is
correctly determined to be �15
�. �15
� or �215�
3 The probabilities are computed correctly, but there are one or two mistakes in thetree diagram.
2 The probabilities are computed correctly, but the tree diagram is incorrect or notgiven. ORThe tree diagram is correct, but only one of the probabilities is computed correctly.
1 The tree diagram is correct, but neither probability is computed correctly. OROne probability is computed correctly, but the other probability and the treediagram are incorrect or not given.
0 Response is completely incorrect.
For Questions 1–3, a bag contains 3 blue, 5 red, and 8 yellow balls. Find each probability if you draw one ball at random from the bag. Write as a fraction insimplest form.
1. P(yellow)
2. P(blue or red)
3. P(not blue)
4. Make a tree diagram on another piece of paper to find the number of ways you can arrange the colors yellow, red, blue,and green if no color can be used more than once. What is the total number of possible arrangements?
5. MULTIPLE CHOICE Supose there are 2 colors (red and blue) for 4 cars (one color per car). Give the total number of possible car-color choices.
A. 4 choices B. 6 choices C. 8 choices D. 10 choices
1.
2.
3.
4.
5.
1. There are 3 paths connecting the library and the post office,2 paths connecting the post office and the bank, and 4 pathsconnecting the bank to home. Find the number of ways towalk from the library to home.
2. SNEAKERS An athletic shoe manufacturer makes sneakers that are white leather or one of three canvas colors with lace-up or Velcro closures. How many different sneakers can be made?
3. In how many ways can a president and vice-president berandomly selected from a class of 28 students?
4. How many permutations are possible of the letters in the word plant?
5. In how many ways can 8 pieces of luggage be arranged on a conveyor belt?
1.
2.
3.
4.
5.
Chapter 9 61 Glencoe California Mathematics, Grade 6
Chapter 9 Quiz 1(Lessons 9-1 and 9-2)
Chapter 9 Quiz 2(Lessons 9-3 and 9-4)
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NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
9
9
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1. ART How many ways can 4 Van Gogh and 5 Monet paintings be hung in 4 spaces if order is not important?
2. CARROTS Austin has 10 carrots and he wants to feed 6 of them to his rabbits. How many ways can he do this?
3. In how many ways can you pick 3 fish from a tank of 9 iforder is not important?
4. Five people are getting into a car. Two people have already claimed the front seats. In how many different ways can the back three seats be taken?
5. There are six finalists in the science fair. In how many different ways can first and second places be awarded?
1.
2.
3.
4.
5.
SHIRTS Grant has 6 different shirts to choose from: maroon,blue, brown, gold, green, and purple.
1. If Grant selects a shirt at random, what is the probability it will be blue or green?
2. If Grant chooses shirts 10 times and chooses the gold one 4 times, what is the experimental probability that the gold shirt is chosen?
3. Find the theoretical probability that a gold shirt is chosen.Discuss any difference between this result and the result found in Question 2.
4. A coin is tossed, and a number cube is rolled. Find P(tails, factor of 12).
5. Four rap CDs, seven dance CDs, two country CDs,three R & B CDs, and five pop CDs are on a shelf.Without replacing the first CD, Ryan takes a second.Find P(R & B, then dance).
1.
2.
3.
4.
5.
Chapter 9 62 Glencoe California Mathematics, Grade 6
Chapter 9 Quiz 3(Lessons 9-5 and 9-6)
Chapter 9 Quiz 4(Lessons 9-7 and 9-8)
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
9
9
Copyright ©
Glencoe/M
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raw-H
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panies, Inc.
Write the letter for the correct answer in the blank at the right of each question.
Use the spinner at the right to find each probability. Write as a fraction in simplest form.
1. P(C)
A. �18� B. �
16
� C. �13�� D. 6
2. P(vowel)
F. �16� G. �
13
� H. �12� J. 3
3. P(not D)
A. 5 B. �56� C. �
58� D. �
16�
4. LETTERS How many permutations are possible of the letters in the word locker?
F. 720 G. 120 H. 21 J. 6
5. ART Eight different color markers are in a box: red, blue, green,yellow, pink, purple, brown, and black. Anne randomly selects two.What is the probability that she selects a red and blue marker?
A. �614� B. �
516� C. �
14
� D. �18
�
6. CONCERT There are four soloists at an orchestra concert. In how many different orders can the musicians play a solo during the evening?F. 4 G. 10 H. 12 J. 24
For each situation, use a tree diagram to find the total number of outcomes.7. tossing a quarter and tossing a penny
8. choosing to watch TV or read a book and choosing pretzels,an apple, or popcorn for a snack
9. choosing a book to read from 5 mysteries and choosing another book to read from 6 biographies
Use the Fundamental Counting Principle to find the total number of outcomes in each situation.10. choosing belt buckles from a collection of 6 bronze,
4 wooden, and 5 silver belt buckles if you choose one of each kind of buckle
11. choosing a school sweatshirt that is gray or white and choosing small, medium, large, or extra-large
12. choosing toast, muffin, or bagel and choosing coffee, milk,or juice
13. choosing an album, CD, and cassette to listen to from a collection of 5 albums, 7 CDs, and 4 cassettes
A
E
F
C
B
D
7.
8.
9.
10.
11.
12.
13.
1.
2.
3.
4.
5.
6.
Chapter 9 Mid-Chapter Test(Lessons 9-1 and 9-4)
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____9
Chapter 9 63 Glencoe California Mathematics, Grade 6
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NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Chapter 9 64 Glencoe California Mathematics, Grade 6
9 Chapter 9 Vocabulary Test
Choose from the terms above to complete each sentence.
1. A(n) _______________ is a possible result.
2. Probability found using frequencies in a game or experimentis called _______________.
3. A(n) _______________ is not affected by the outcome of theprevious event.
4. The set of all possible outcomes is called the _______________.
5. A(n) _______________ is one of two events that are the onlyones that can possibly happen and the sum of whose probabilities is 1.
6. A(n) _______________ is an arrangement, or listing, of objectsin which order is important.
7. The chance of an event happening is called _______________.
8. A(n) _______________ is an arrangement, or listing, in which order is not important.
9. In a _______________, all players of equal skill have an equal chance of winning.
10. A(n) _______________ is made up of two or more simple events.
Define the term in your own words.
11. Fundamental Counting Principle
combination complementary events compound events experimental probability fair game Fundamental Counting Principle independent events outcome
permutation probability random sample space simple event theoretical probability tree diagram
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Write the letter for the correct answer in the blank at the right of each question.
1. How many different 4-digit numbers are there if no digit is repeated?A. 4 B. 24 C. 504 D. 4,536
2. In how many ways can you choose 2 side dishes out of 8?F. 56 G. 28 H. 16 J. 4
DOGS The boarders at a kennel are made up of the following dogs. If one dog is randomly selected for a 30-minute training session, find theprobability of each event. The fractions are written in simplest form.
3. P(retriever)
A. �34� B. �
35� C. �
12� D. �
38�
4. P(not male)
F. �1294�
G. �172�
H. �12� J. �2
74�
5. P(cat)
A. 0 B. �1100�
C. �12� D. 1
For Questions 6–8, use the Fundamental Counting Principle to find thetotal number of outcomes in each situation.
6. tossing a quarter and a pennyF. 1 G. 2 H. 4 J. 8
7. choosing a meat, a vegetable, and a beverage from 3 kinds of meat, 2 kinds of vegetables, and 4 kinds of beveragesA. 9 B. 10 C. 24 D. 48
8. picking a day of the week and rolling a number cubeF. 13 G. 14 H. 30 J. 42
9. A blue number cube and an orange number cube are rolled.Find P(3, then even).
A. �65� B. �
23� C. �
16� D. �1
12�
10. A bag contains 3 orange, 5 black, and 2 white marbles. Two marbles aredrawn, but the first marble is not replaced. Find P(white, then black).
F. �59� G. �
19� H. �1
10�
J. �115�
Use a tree diagram.
11. TESTS Justine is taking a test with four true/false questions. How many possible ways can the four answers appear on the test? A. 4 B. 8 C. 16 D. 32
12. RINGS Lianna has enough money to buy one ring. She can choose a silver or a gold band and an onyx, opal, or topaz setting. From how many different combinations does she have to choose?F. 2 G. 4 H. 6 J. 8
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Ass
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Chapter 9 65 Glencoe California Mathematics, Grade 6
9NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Chapter 9 Test, Form 1C
opyr
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Com
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Inc.
BoardersMales 10Females 14Pointers 6Retrievers 18
Tell whether each problem represents a permutation (P) or a combination (C). Then solve the problem.
13. Ten students remain in a game of musical chairs. If four chairs are removed, how many different groups of six students can remain?A. P; 65 B. C; 105 C. C; 210 D. C; 420
14. How many different ways can five airplanes be arranged at five gates?F. C; 5 G. C; 24 H. P; 96 J. P; 120
15. In how many ways can Zoe choose 4 figurines from a collection of 7?A. C; 11 B. C; 28 C. C; 35 D. P; 5,040
16. RACING In a cross-country race with 8 runners, how many different ways can they come across the finish line?F. P; 40,320 G. P; 5,760 H. C; 1,120 J. C; 36
BASEBALL Corey has two tickets to a baseball game. He can take one of hisfriends with him, but five of his friends would like to go. They are Jane,Meg, Matt, Ted, and Amy. To decide, Corey writes each of his friends’names on a separate piece of paper and selects one.
17. What is the probability that Corey picks a boy?
A. �15� B. �
25� C. �
35� D. �
23�
18. What is the probability that Corey picks someone whose name does not beginwith the letter M?
F. �35� G. �
25� H. �
15� J. �
16�
19. If Corey draws a name 20 times and Amy’s name is picked twice, what is theexperimental probability that Amy’s name is picked?
A. �25� B. �
15� C. �
16� D. �1
10�
20. Choose the best comparison between the theoretical and experimentalprobability that Amy will go to the game. Use the experimental probabilityfrom Question 19.F. The theoretical probability is greater than the experimental probability.G. The theoretical probability is less than the experimental probability.H. The theoretical probability is equal to the experimental probability.J. The theoretical probability is not related to the experimental probability.
Bonus CLASSES Tim can select 4 of his classes from the following options: algebra, American Sign Language, typing, English,Spanish, tennis, and science. What is the probability that Tim will select science, algebra, typing, and Spanish?
13.
14.
15.
16.
17.
18.
19.
20.
B:
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 9 66 Glencoe California Mathematics, Grade 6
9 Chapter 9 Test, Form 1 (continued)C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
cGraw
-Hill C
ompanies, Inc.
Write the letter for the correct answer in the blank at the right of each question.
1. How many different 5-digit numbers are there if no digit is repeated?A. 120 B. 720 C. 15,120 D. 27,216
2. In how many ways can you choose 2 side dishes out of 9?F. 72 G. 36 H. 18 J. 9
DOGS The boarders at a kennel are made up of the following dogs. If one dog is randomly selected for a 30-minute training session, find the probability of each event. The fractions are written in simplest form.
3. P(female)
A. �172�
B. �12� C. �1
77�
D. �274�
4. P(not pointer)
F. �38� G. �
12� H. �
34� J. �
78�
5. P(pointer or retriever)
A. 24 B. 1 C. �12� D. 0
For Questions 6–8, use the Fundamental Counting Principle to find the total number of outcomes in each situation.
6. tossing a nickel, a quarter, a penny, and rolling a number cubeF. 4 G. 12 H. 24 J. 48
7. choosing coffee or tea, with cream, milk, or honey served in a glass or a plastic cupA. 24 B. 12 C. 7 D. 6
8. picking a number from 1 to 20 and a letter from the alphabetF. 520 G. 260 H. 46 J. 4
9. The spinner at the right has an equal chance of landing on each number. Find P(6, then 6).
A. �419�
B. �211�
C. �110�
D. �27�
10. There are 5 peppermint, 4 licorice, 8 grape, 2 orange, and 9 cherry jelly beans in a bag. Paco picks a jelly bean. Without replacing the first one, he picks a second jelly bean. Find P(grape, then cherry).
F. �89� G. �2
21�
H. �11425�
J. �1125�
Use a tree diagram.
11. CLOTHING Janet has 4 blouses, 2 pairs of pants, and 3 pairs of socks that can be worn together. How many outfits can she make?A. 9 B. 18 C. 20 D. 24
12. TRAILS At Brand-X Ranch you can ride the Buckin’ Billy, Tennessee Lady, or Lag-Behind Nell. One trail goes through the woods, another goes up a mountain,and a third trail goes by a stream. How many different horse rides can you take?F. 3 G. 6 H. 9 J. 12
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Chapter 9 67 Glencoe California Mathematics, Grade 6
9NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Chapter 9 Test, Form 2AC
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BoardersMales 10Females 14Pointers 6Retrievers 18
Tell whether each problem represents a permutation (P) or a combination (C). Then solve the problem.
13. Twelve students remain in a game of tag. If 6 students go out in the next minute, how many different groups of six students can remain?A. C; 924 B. P; 1,140 C. C; 1,638 D. P; 665,280
14. Brandon has 8 different plates with which to set the table. How many different ways can he place the plates?F. C; 36 G. C; 336 H. P; 6,720 J. P; 40,320
15. In how many ways can Mia choose 10 mugs from a collection of 15?A. C; 360,360 B. C; 3,003 C. C; 150 D. P; 105
16. BAND How many ways can 7 clarinet players be seated in 7 chairs in the concert band?F. P; 56 G. C; 792 H. P; 5,040 J. C; 823,543
FOOTBALL Tori has four tickets to a football game. She can take three ofher friends with her, but five of her friends would like to go. They areTom, Jill, Joe, Marvin, and Ginger. To decide, Tori writes each of herfriends’ names on a separate piece of paper and selects one.
17. What is the probability that Tori picks a boy?
A. �15� B. �
25� C. �
35� D. �
23�
18. What is the probability that Tori picks someone whose name begins with theletter J?
F. �35� G. �
12� H. �
25� J. �
16�
19. If Tori draws a name 15 times and Tom’s name is picked five times, what is the experimental probability that Tom’s name is picked?
A. �55� B. �
56� C. �
13� D. �
15�
20. Choose the best comparison between the theoretical and experimental probability that Tom will go to the game. Use the experimental probability from Question 19.F. The theoretical probability is greater than the experimental probability.G. The theoretical probability is less than the experimental probability.H. The theoretical probability is equal to the experimental probability.J. The theoretical probability is not related to the experimental probability.
Bonus CLASSES Ishi can select 3 of her classes from the following options: French, Spanish, German, art, band,and consumer science. What is the probability that Ishi will select French, art, and band?
13.
14.
15.
16.
17.
18.
19.
20.
B:
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 9 68 Glencoe California Mathematics, Grade 6
9 Chapter 9 Test, Form 2A (continued)C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
cGraw
-Hill C
ompanies, Inc.
Write the letter for the correct answer in the blank at the right of each question.
1. How many different 5-letter passwords can be made using the letters A, E, I, O, and U if no letter is repeated?A. 4 B. 24 C. 25 D. 120
2. In how many ways can you choose 2 side dishes out of 10?F. 180 G. 90 H. 45 J. 20
DOGS The boarders at a kennel are made up of the following dogs. If one dog is randomly selected for a 30-minute training session, find the probability of each event. The fractions are written in simplest form.
3. P(male)
A. �57� B. �
12� C. �1
52�
D. �254�
4. P(not retriever)
F. �58� G. �
13� H. �
14� J. �
18�
5. P(male or female)
A. 0 B. 1 C. �12� D. 24
For Questions 6–8, use the Fundamental Counting Principle to find the total number of outcomes in each situation.
6. tossing a dime, a quarter, a penny, and a nickel and rolling a number cubeF. 5 G. 14 H. 48 J. 96
7. choosing iced tea or lemonade, with lemon or lime twist, served in small,medium, or large size glassesA. 6 B. 7 C. 12 D. 24
8. picking a number from 1 to 30 and a letter from the alphabetF. 780 G. 390 H. 56 J. 4
9. The spinner at the right has an equal chance of landing on each number. Find P(an odd number, then an even number).
A. �77� B. �
1429�
C. �479�
D. �429�
10. There are 2 bunny counters, 16 mouse counters, 8 snake counters, and 7 monkey counters in the bag. Gina takes 2 counters without replacing the first counter. Find P(snake, then bunny).
F. �1616�
G. �116�
H. �313�
J. �616�
Use a tree diagram.
11. EQUIPMENT Raymond has 4 mouth guards, 5 pairs of shin guards, and 3 pairs of turf shoes. How many different combinations of sports equipment can he wear if he wears one of each type?A. 60 B. 50 C. 20 D. 15
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Chapter 9 69 Glencoe California Mathematics, Grade 6
9NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Chapter 9 Test, Form 2BC
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BoardersMales 10Females 14Pointers 6Retrievers 18
12. SPORTS If there are 8 footballs and 4 basketballs, how many different wayscould you choose 1 football and 1 basketball?F. 8 G. 12 H. 24 J. 32
Tell whether each problem represents a permutation (P) or a combination (C). Then solve the problem.13. Twenty students remain in a spelling bee. If 7 students misspell words in
the next round, how many different groups of 13 contestants can remain?A. C; 390,700,800 B. C; 77,520 C. P; 5,040 D. P; 1,820
14. How many different ways can Dana arrange 9 pairs of shoes in a row?F. C; 45 G. P; 3,039 H. C; 60,480 J. P; 362,880
15. In how many ways can Justin choose 11 cars from a collection of 20?A. P; 39,916,800 B. C; 167,960 C. C; 10,890 D. P; 110
16. How many different ways can Cora give 10 stuffed animals to the 10 guests at her birthday party?F. P; 3,628,800 G. P; 80,640 H. C; 65,978 J. C; 155
SOCCER Noriko has four tickets to a soccer game. She can take three of her friends with her, but seven would like to go. They are Isabel, Dan,Joni, Ike, Xavier, Patti, and Ian. To decide, Noriko writes each of her friends’ names on a separate piece of paper and selects one.17. What is the probability that Noriko picks a boy?
A. �23� B. �
47� C. �
37� D. �
17�
18. What is the probability that Noriko picks someone whose name begins with the letter I?
F. �27� G. �
37� H. �
47� J. �
57�
19. If Noriko draws a name 20 times and Patti’s name is picked six times, what is the experimental probability that Patti’s name is chosen?
A. �14� B. �1
30�
C. �270�
D. �67�
20. Choose the best comparison between the theoretical and experimental probability that Patti will go to the game. Use the experimental probability from Question 17.F. The theoretical probability is greater than the experimental probability.G. The theoretical probability is less than the experimental probability.H. The theoretical probability is equal to the experimental probability.J. The theoretical probability is not related to the experimental probability.
Bonus CLASSES Carol can select two classes from these options:French, Spanish, consumer science, industrial technology,art, and music. What is the probability that Carol will select industrial technology and music? B:
12.
13.
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15.
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17.
18.
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NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 9 70 Glencoe California Mathematics, Grade 6
9 Chapter 9 Test, Form 2B (continued)C
opyright ©G
lencoe/McG
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cGraw
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ompanies, Inc.
1. On another piece of paper, make a tree diagram to find how many different ways you can arrange the letters C, A, R, and S, if you use each letter once. How many ways are possible?
2. CRAFT Rodrigo is making round, square, and rectangular window ornaments. He cuts some from origami paper and others from old wallpaper. He then paints them either red or green. Make a tree diagram on another piece of paper to find how many different kinds of ornaments Rodrigo can make.What is the total number of ornaments?
Use the spinner to find each probability.Write as a fraction in simplest form.
3. P(even number)
4. P(2 or 3)
Use the Fundamental Counting Principle to find the total number of outcomes in each situation.
5. buying bedroom furniture if you can select one each from 7 dressers, 4 beds, 6 lamps, and 9 night tables
6. choosing one of each kind of pet from 8 hamsters, 3 guinea pigs, and 10 gerbils
7. the total number of sharks tagged in 6 days by 8 scientists if each scientist tags 3 new sharks every day
Tell whether each problem represents a permutation or a combination. Then solve the problem.
8. RACING In how many ways can 7 runners finish first,second, and third in a race?
9. How many different two-topping ice cream sundaes are available if there are 6 toppings to choose from?
10. In how many ways can you choose a committee of four people from the nine in the club?
11. How many different 3-digit codes can be created if no digit can be repeated?
8 1
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Chapter 9 71 Glencoe California Mathematics, Grade 6
9NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Chapter 9 Test, Form 2CC
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12. How many 6-digit numbers are there if no digit is repeated?
13. DESIGN In how many ways can you choose 2 colors for a design out of 14 colors?
CARPOOL Angie can fit 5 people in her van but 7 of her friends want to ride with her to the lacrosse game. Her friends are Sara, Penny, Geoff, Greg, Kimberly, Phil, and Lester. To decide, Angie writes each of her friends’ names on a separate piece of paper and selects one.
14. What is the probability that Angie picks a girl?
15. What is the probability that Angie picks someone whose name begins with the letter G or P?
16. If Angie picks a name 18 times and Sara’s name is picked 10 times, what is the experimental probability that Sara’s name is picked?
17. How does the theoretical probability that Sara will get a ride compare to the experimental probability in Question 16?
Find each probability.
18. PENS Gwen has 4 blue pens, 8 black pens, 2 green pens, and 3 red pens in her desk drawer. She takes out two pens without replacing the first pen. Find P(green, then blue).
19. BEARS Giovanni has a bag of 17 wooden beads, 1 flowered bead, 4 tie-dyed beads, and 10 red beads. After replacing his first bead, he pulls out a second bead. Find P(tie-dyed,then flowered).
20. APPLES Melody’s dad brought home a crate of apples he picked from their orchards. The crate contained 10 Granny Smiths, 14 Red Delicious, 4 Golden Delicious, and 18 Braeburns.Without replacing the first apple, she took out a second apple. Find P(Golden Delicious, then Braeburn).
Bonus PASSWORDS Determine the number of passwords that can be made from 2 letters followed by 4 digits if no letter or digit can be used more than once.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 9 72 Glencoe California Mathematics, Grade 6
9 Chapter 9 Test, Form 2C (continued)C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
cGraw
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ompanies, Inc.
1. On another piece of paper, make a tree diagram to find how many different ways you can arrange red, yellow, blue, and green colored pencils in a 4-pencil holder. How many arrangements are there?
2. LUNCH Barry sells hot dogs with or without mustard. Hiscustomers can also choose potato chips, corn chips, or pretzels.Make a tree diagram on another piece of paper to find out how many different orders Barry might receive if customers choose one type of hot dog and one type of chip or pretzel. How many different kinds of orders might Barry receive?
Use the spinner to find each probability.Write as a fraction in simplest form.
3. P(odd number)
4. P(4, or 5)
Use the Fundamental Counting Principle to find the total number of outcomes in each situation.
5. total number of trees planted in 5 days by 30 people, whoeach plant 3 trees per day
6. total number of disguises you can create with 2 different contact-lens colors, 3 different wigs, 2 different noses, and 1 mustache if one of each is chosen
7. choosing an outfit from 2 different hats, 3 pairs of pants,3 pairs of shoes, and a shirt if one of each is chosen
Tell whether each problem represents a permutation or a combination. Then solve the problem.
8. In how many ways can you select three classes from a total of 10 being offered?
9. How many ways can a president and vice-president bechosen from a committee of 8 members?
10. How many ways can 5 models line up to have their picture taken?
11. How many different 3-flavor shakes are available if there are 7 flavors of ice cream available?
8 1
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Chapter 9 73 Glencoe California Mathematics, Grade 6
9NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Chapter 9 Test, Form 2DC
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Find the value of each expression.
12. How many different 7-digit numbers are there if no digitsis repeated?
13. DESIGN In how many ways can you choose 3 colors for a design out of 11 colors?
CARPOOL Luis can fit 3 people in his car, including himself,but 5 of his friends want to ride with him to the track meet. His friends are Tim, Maria, Lilly, Katey, and Ruben.To decide, Luis writes each of his friends’ names on a separate piece of paper and selects one.
14. What is the probability that Luis picks a girl?
15. What is the probability that Luis picks someone whose name ends with the letter Y?
16. If Luis picks a name 12 times and Ruben’s name is picked 4 times, what is the experimental probability that Ruben’s name is picked?
17. How does the theoretical probability that Ruben will get a ride compare to the experimental probability in Question 16?
Find each probability.
18. PETS Yvonne is playing with her gerbils. She has 4 white,3 brown, and 1 gray gerbil. Without replacing the first one,she takes a second gerbil out of the cage. Find P(white,then gray).
19. CLOTHES Andrew has 3 pairs of jeans shorts, 1 pair of camouflage shorts, and 2 pairs of black shorts in a drawer.He chooses one pair, puts them back and chooses another.Find P(jeans, then camouflage).
20. PUPPETS Shari has 4 lamb puppets, 5 horse puppets, and 2 dog puppets in a bag. Without replacing the first, she takes out a second puppet. Find P(horse, then lamb).
Bonus PASSWORDS Determine the number of passwords that can be made from 2 letters followed by 3 digits if no letter or digit can be used more than once.
12.
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18.
19.
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NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 9 74 Glencoe California Mathematics, Grade 6
9 Chapter 9 Test, Form 2D (continued)C
opyright ©G
lencoe/McG
raw-H
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cGraw
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ompanies, Inc.
1. On another piece of paper, make a tree diagram to find how many different ways you can arrange the numbers 1, 4, and 5 if no number can be used more than once. How many arrangements are there?
2. MUSIC Angela is deciding which song to play next. She can choose one that is fast or slow, current or old, and Country or Top 40. Make a tree diagram on another piece of paper to find how many types of songs she can choose from. How many types are there?
Use the spinner to find each probability.Write as a fraction in simplest form.
3. P(number less than 5)
4. P(even number or 7)
Use the Fundamental Counting Principle to find the total number of outcomes in each situation.
5. total number of toads found by 21 scientists in 3 days if each scientist finds 7 new toads each day
6. choosing one of each kind of ball from 4 glowballs,15 superballs, and 8 moonballs
7. choosing one of each color paint from 3 yellow paints,4 green paints, and 2 white paints
Tell whether each problem represents a permutation or a combination. Then solve the problem.
8. How many ways can 6 family photos be set in a line on a fireplace mantel?
9. How many different 4-topping salads are available if there are 8 toppings to choose from?
10. How many ways can you pick 3 kittens from a litter of 7 kittens?
11. How many different 3-letter security passwords can be created if no letter can be repeated?
8 1
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Chapter 9 75 Glencoe California Mathematics, Grade 6
9NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Chapter 9 Test, Form 3C
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Find the value of each expression.
12. How many different passwords are there if the first two characters are two different letters and the last 4 characters are digits, where no digit is repeated?
13. FOOD In how many ways can you choose 3 side dishes from 12 choices?
CARPOOL Misu can fit 3 other people into his car but 5 of his friends want to get a ride to the baseball game. His friends are Brittany, Anne, Steve, Monique, and John. To decide,Misu writes each of his friends’ names on a separate piece of paper and selects one.
14. What is the probability that Misu picks a girl?
15. What is the probability that Misu picks someone whose name ends with the letter E?
16. If Misu chooses a name 16 times and Monique’s name is picked 6 times, what is the experimental probability that Monique’s name is picked?
17. How does the theoretical probability that Monique will get a ride compare to the experimental probability in Question 16?
Find each probability.
18. BASKETBALL Rita has a record of making 2 out of every 5 free throws. What is the probability that she will make both of her next two free throws?
19. TESTS On a math test, 5 out of 20 students got an A. If three of the 20 students are chosen at random, what is the probability that all three got an A on the test?
20. Three cards are chosen at random from a standard deck of cards without replacement. What is the probability of getting 3 aces?
Bonus PASSWORDS Determine the number of passwords that can be made from 3 letters followed by 3 digits if no letter or digit can be used more than once and the digit 0 cannot be used.
12.
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14.
15.
16.
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18.
19.
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NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 9 76 Glencoe California Mathematics, Grade 6
9 Chapter 9 Test, Form 3 (continued)C
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lencoe/McG
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Demonstrate your knowledge by giving a clear, concise solution toeach problem. Be sure to include all relevant drawings and justifyyour answers. You may show your solutions in more than one wayor investigate beyond the requirements of the problem. If necessary,record your answer on another piece of paper.
1. Seven Oaks Middle School is having its Spring fair.
a. A game uses spinner A below. If a player spins a 1, he or she wins aprize. Explain how to find the theoretical probability of winning aprize.
Spinner A Spinner B
b. A second game uses spinner B. A player must spin a W to win.Explain how to find the experimental probability of spinning a W.
2. A bag contains 1 white (W), 3 blue (B1, B2, B3), and 2 red (R1, R2)marbles.
a. Use a tree diagram to list all of the possible outcomes for tossing acoin and then drawing a marble from the bag.
b. Explain what is meant by independent events.
c. Find the probability of tossing a head and drawing a red marble.Explain you reasoning.
d. Find the probability of drawing two blue marbles if the first marble isnot replaced. Explain each step.
3. Rayna and her husband have 8 nieces, 9 nephews, 6 cousins, 3 aunts, and5 uncles.
a. Explain how you could use the Fundamental Counting Principle tofind how many ways Rayna could choose a team to play charades ifshe wants one of each type of relative on the team.
b. How many ways could just the nieces stand in line to limbo? Explainyour method.
c. If everyone except Rayna and her husband wants to play musicalchairs but there are only 10 chairs available, how many ways could 10of the relatives sit in the chairs when the music stops? Explain yourmethod.
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Chapter 9 77 Glencoe California Mathematics, Grade 6
9NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Chapter 9 Extended-Response Test
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1. Which equation could be used to find the width of a rectangle with a perimeter of 80 inches and a length of 25 inches? (Lesson 3-2)
A 80 � 25 � �w2� C 80 � 25 � w
B 80 � 50 � 2w D 80 � 50 � 2w
2. Solve w � 7.3 � 12.8. (Lesson 3-2)
F �20.1 G 5.5 H 14.6 J 20.1
3. Find the GCF of 30 and 42. (Lesson 4-2)
A 2 B 3 C 6 D 210
4. Write �290� as a percent. (Lesson 4-6)
F 0.45% G 4.5% H 45% J 450%
5. Find �196� � �
14
�. (Lesson 5-2)
A �14
� B �156� C �
12
� D �1136�
6. What is �38
� � �58
�? (Lesson 5-5)
F �1654� G �
35
� H �1156� J 1
7. Solve �12�k � �
27�. Check your solution. (Lesson 5-6)
A 7 B �74� C �
47� D �
17�
8. Write the ratio 2�23� yards to 4 feet as a fraction in simplest form.
(Lesson 6-1)
F �12� G �
23� H �
24.7� J �
21�
9. Solve the proportion: �83� � �
2w0�. (Lesson 6-5)
A �125�
B 1.2 C 7.5 D 53�13�
10. LAYAWAY Angie wants to put a winter coat on layaway at a store. To do so, she must pay the store 20% of the cost of the coat so they will hold it. If the coat costs $125, how much of a deposit does Angie need to pay the store? (Lesson 7-2)
F $250 G $25 H $12.50 J $2.50
11. Find the sales tax to the nearest cent on a $25 pair of shoes with 5.75% sales tax. (Lesson 7-7)
A $1.43 B $1.44 C $1.77 D $5.75
12. Find the simple interest to the nearest cent for a principal of $4,329, an interest rate of 9.25%, and a time period of 18 months. (Lesson 7-8)
F $7,207.79 G $4,929.94 H $4,356.25 J $600.65
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12. F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Chapter 9 78 Glencoe California Mathematics, Grade 6
9 Standardized Test Practice(Chapters 1–9)
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
13. SOFTWARE The data in the table shows the prices of the top-selling business software. Find the medianof the data. (Lesson 8-2)
A $53B $71.30C $183D $201
14. To determine the most popular kind of music in California,a survey of 100 randomly selected households in Sacramento is conducted. Of the households, 34 chose pop music. The researcher concluded that 34% of California households prefer pop music. Which of the following methods did the researcher use? (Lesson 8-8)
F simple random surveyG systematic random sampleH convenience sampleJ stratified random sample
15. GAMES Gene made up a game where each player tosses two coins and a number cube. Use a tree diagram to find how many outcomes are possible. (Lesson 9-2)
A 6 B 24 C 30 D 36
16. If there are 6 baseballs, 10 tennis balls, and 11 golf balls available, how many different combinations of balls could be made if one of each type is chosen? (Lesson 9-3)
F 660 G 66 H 60 J 27
17. SALAD BARS If Philip made three trips to a salad bar with 10 different items and chose only one different item each time, in how many ways could he have selected his food? (Lesson 9-5)
A 1,000 B 720 C 120 D 30
18. A water cooler holds 3 gallons of water.How many cups does the cooler hold? (Lesson 6-3)
F 12 G 24 H 48 J 60
19. How many different ways can 6 notebooks be arranged on a shelf? (Lesson 9-4)
A 4,320 B 720 C 216 D 36
13.
14.
15.
16.
17.
18.
19. A B C D
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
Ass
essm
ent
Chapter 9 79 Glencoe California Mathematics, Grade 6
9NAME ________________________________________ DATE ______________ PERIOD _____
Standardized Test Practice (continued)
(Chapters 1–9)
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
Software Prices ($)
218 .89 86 19
201 115 36 53
253 243
20. Find 3 � (�17). (Lesson 2-5)
21. Write 16% as a fraction in simplest form. (Lesson 4-6)
22. Find 2�34� � 2. Write in simplest form. (Lesson 5-7)
23. LANDFILLS The graph shows the content in U.S. landfills.How much more plastic isthere than food and yardwaste? (Lesson 8-4)
24. ASSIGNMENTS Linda must finish 7 projects from a list of 13for her industrial technology class. In how many ways canLinda do this if the order is not important? (Lesson 9-5)
25. PHOTOGRAPHY Paul is the photographer hired for a wedding.He is arranging 3 women, 3 men, and 2 children in a line for a picture. (Lesson 9-4)
a. How many ways can he arrange them if he wants them in the following order: child, woman, man, woman, man,woman, man, child? Explain.
b. How many ways can he arrange all of the people if the order of women, men, and children does not matter? Explain.
Other
Food
& Ya
rd W
aste
Rubb
er &
Leath
er
Metal
15
20
10
0
5
25
30
35
Perc
ent
Plasti
cPa
per
U.S. Landfill Content
8%
24%
6%
11%
30%
21%
Part 2: Short Response
Instructions: Write answers to short responses in the space provided.
20.
21.
22.
23.
24.
25a.
25b.
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 9 80 Glencoe California Mathematics, Grade 6
9 Standardized Test Practice (continued)
(Chapters 1–9)
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
MILES PER HOUR For Questions 1–3, use the line plot that shows the speeds (in miles per hour) of 40 cars traveling on the freeway. (Lesson 2-3)
1. What is the range of the data?
2. What speed occurred most often?
3. Identify any clusters, gaps, or outliers.
4. RAINFALL The graph shows theaverage rainfall in Minneapolis,Minnesota, each month fromMarch to June. Predict theaverage rainfall for July.
5. Find the mean, median, and mode for the data.
$5, $9, $13, $7, $6, $5, $11
6. Make a stem-and-leaf plot for the data.
25, 35, 43, 50, 56,38, 45, 29, 40, 47
7. TESTS The data shows the quiz scores earned by students in a science class. What is the median?
8. TELEVISIONS The graph shows the countries withthe most televisions percapita. Why might thisgraph be consideredmisleading?
UKJapanCanadaUSA
700
900
800
600Tele
visi
ons
per 1
000
Peop
le
Australia
Countries with the MostTelevisions per Capita
Mar. Apr. May June
60
40
20
80
100
120
Aver
age
Rain
fall
(mm
)
Month
0
Rainfall in Minneapolis, MN
1.
2.
3.
4.
5.
6.
7.
8.
Ass
essm
ent
Chapter 9 81 Glencoe California Mathematics, Grade 6
9NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Unit 4 Test(Chapters 8 and 9)
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
64 66 68 70 72 74 76 78 8062
�
���
��
�������
����
�����
�����
����
��� � �
��
��
Quiz Scores
18 17 20 10 1519 0 13 17 1417 20 11 10 9
9. A number cube is rolled two times. Find the probability of rolling an odd number then an even number.
10. A card is drawn from a standard deck of 52 cards.A second card is drawn without replacing the first card.Find P(black card, then red card).
For Questions 11–13, a set of 12 cards is numbered 1, 2, 3, ... , 12. Suppose you pick a card at random without looking. Find the probability of each event.Write as a fraction in simplest form.
11. P(5 or 7)
12. P(multiple of 3)
13. P(not an even number)
Use the spinner to find each probability. Write as a fractionin simplest form.
14. P(E)
15. P(not a vowel)
16. Make a tree diagram on another piece of paper to show the sample space for picking a number from 1 to 6 and choosing a color yellow, purple, or green. Then give the total number of outcomes.
17. Use the Fundamental Counting Principle to find the totalnumber of outcomes in the following situation. Find the totalnumber of cans of food donated to the Hunger Taskforce by40 people in 17 days if each person donates 2 cans every day.
For Questions 18 and 19, tell whether each problem represents a permutation or combination. Then solve the problem.
18. How many different ways can you choose 5 books from a total of 15 books?
19. How many different ways can 11 board games be stacked?
20. Tell whether the following event is independent or dependent.Then find the probability. Choose a particular male from 20 males and a particular female from 10 females.
A
E
F
C
B
D
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 9 82 Glencoe California Mathematics, Grade 6
9 Unit 4 Test (continued)
(Chapters 8 and 9)
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
An
swer
s
pygp
Lesson 9–1
Cha
pter
99
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n a
t th
e to
p o
f p
age
460
in y
our
text
boo
k.W
rite
you
r an
swer
s b
elow
.
1.W
hat
fra
ctio
n o
f th
e ta
ffy
is v
anil
la?
Wri
te i
n s
impl
est
form
.�1 8�
2.S
upp
ose
you
tak
e on
e pi
ece
of t
affy
fro
m t
he
box
wit
hou
t lo
okin
g.A
reyo
ur
chan
ces
of p
icki
ng
van
illa
th
e sa
me
as p
icki
ng
root
bee
r? E
xpla
in.
Sam
ple
an
swer
:Yes
;th
ere
is t
he
sam
e n
um
ber
of
van
illa
pie
ces
as r
oo
t b
eer
pie
ces.
Rea
d t
he
Less
on
Use
th
e in
form
atio
n f
rom
th
e in
trod
uct
ion
to
answ
er E
xerc
ises
3–5
.
3.H
ow d
o yo
u r
ead
P(c
her
ry)?
the
pro
bab
ility
of
pic
kin
g a
pie
ce o
fch
erry
taf
fy
4.P
(ch
erry
) �
� 46 8�;w
her
e do
es t
he
6 co
me
from
? W
her
e do
es t
he
48 c
ome
from
?6
�th
e n
um
ber
of
pie
ces
of
cher
ry t
affy
;48
�th
eto
tal n
um
ber
of
pie
ces
of
taff
y
5.P
roba
bili
ty c
an b
e w
ritt
en a
s a
frac
tion
,a d
ecim
al,o
r a
perc
ent.
Wri
teP
(ch
erry
) as
a d
ecim
al.
0.12
5
6.If
th
ere
is a
25%
ch
ance
th
at s
omet
hin
g w
ill
hap
pen
,wh
at i
s th
e ch
ance
that
it
wil
l n
oth
appe
n?
Wh
at a
re t
hes
e tw
o ev
ents
cal
led?
75%
;co
mp
lem
enta
ry e
ven
ts
Rem
emb
er W
hat
Yo
u L
earn
ed7.
Wri
te t
he
equ
atio
n P
(A)
�P
(not
A)
�1
in w
ords
.Wh
at d
oes
it m
ean
wit
hre
spec
t to
eve
nt
A?
Sam
ple
an
swer
:Th
e p
rob
abili
ty o
f A
eit
her
hap
pen
ing
or
no
t h
app
enin
g is
eq
ual
to
1;
it is
cer
tain
th
atev
ent
A w
ill e
ith
er h
app
en o
r n
ot
hap
pen
.
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Less
on R
eadi
ng G
uide
Sim
ple
Eve
nts
9-1
6SD
AP
3.3
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Ant
icip
atio
n Gu
ide
Pro
bab
ility
Cha
pter
97
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Chapter Resources
pygp
9
Bef
ore
you
beg
in C
ha
pte
r 9
•R
ead
each
sta
tem
ent.
•D
ecid
e w
het
her
you
Agr
ee (
A)
or D
isag
ree
(D)
wit
h t
he
stat
emen
t.
•W
rite
A o
r D
in
th
e fi
rst
colu
mn
OR
if
you
are
not
su
re w
het
her
you
agr
ee o
r di
sagr
ee,w
rite
NS
(N
ot S
ure
).
Aft
er y
ou c
omp
lete
Ch
ap
ter
9
•R
erea
d ea
ch s
tate
men
t an
d co
mpl
ete
the
last
col
um
n b
y en
teri
ng
an A
or
a D
.
•D
id a
ny
of y
our
opin
ion
s ab
out
the
stat
emen
ts c
han
ge f
rom
th
e fi
rst
colu
mn
?
•F
or t
hos
e st
atem
ents
th
at y
ou m
ark
wit
h a
D,u
se a
pie
ce o
f pa
per
to w
rite
an
ex
ampl
e of
wh
y yo
u d
isag
ree.
Step
2
Step
1
ST
EP
1S
tate
men
tS
TE
P 2
A,D
,or
NS
A o
r D
1.T
he
prob
abil
ity
of a
n e
ven
t h
appe
nin
g is
a r
atio
th
at
com
pare
s th
e n
um
ber
of f
avor
able
ou
tcom
es t
o th
e n
um
ber
Dof
un
favo
rabl
e ou
tcom
es.
2.If
th
e pr
obab
ilit
y of
an
eve
nt
hap
pen
ing
is �3 5�
then
it
is m
ore
Ali
kely
for
th
e ev
ent
to h
appe
n t
han
to
not
hap
pen
.3.
In a
pro
babi
lity
exp
erim
ent,
a tr
ee d
iagr
am c
an b
e u
sed
to
Ash
ow a
ll t
he
poss
ible
ou
tcom
es.
4.T
he
Fu
nda
men
tal
Cou
nti
ng
Pri
nci
ple
stat
es t
hat
th
e n
um
ber
Dof
pos
sibl
e ou
tcom
es c
an a
lso
be f
oun
d by
div
isio
n.
5.T
o fi
nd
the
valu
e of
4!,
add
4�
3�
2�
1.D
6.In
a c
ombi
nat
ion
,ch
oosi
ng
even
t A
then
eve
nt
Bw
ould
be
Ath
e sa
me
as c
hoo
sin
g ev
ent
Bth
en e
ven
t A
.
7.T
he
expe
rim
enta
l pr
obab
ilit
y of
an
eve
nt
hap
pen
ing
wil
l al
way
s be
clo
se t
o th
e th
eore
tica
l pr
obab
ilit
y of
th
at e
ven
t D
hap
pen
ing.
8.T
he
act
it o
ut
stra
tegy
is
a go
od w
ay t
o so
lve
prob
lem
s be
cau
se t
he
resu
lts
wil
l be
th
e sa
me
ever
y ti
me
the
Dex
peri
men
t is
rep
eate
d.9.
A c
ompo
un
d ev
ent
con
sist
s of
tw
o or
mor
e si
mpl
e ev
ents
.A
10.
Th
e pr
obab
ilit
y of
tw
o in
depe
nde
nt
even
ts i
s fo
un
d th
e sa
me
Dw
ay a
s th
e pr
obab
ilit
y of
tw
o de
pen
den
t ev
ents
.
Answers (Anticipation Guide and Lesson 9-1)
Chapter 9 A1 Glencoe California Mathematics, Grade 6
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Skill
s Pr
actic
eS
imp
le E
ven
ts
Cha
pter
911
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Lesson 9–1
pygp
9-1
A s
et o
f 12
car
ds
is n
um
ber
ed 1
,2,3
,…12
.Su
pp
ose
you
pic
k a
car
d a
tra
nd
om w
ith
out
look
ing.
Fin
d t
he
pro
bab
ilit
y of
eac
h e
ven
t.W
rite
as
a fr
acti
on i
n s
imp
lest
for
m.
1.P
(5)
� 11 2�2.
P(6
or
8)�1 6�
3.P
(a m
ult
iple
of
3)�1 3�
4.P
(an
eve
n n
um
ber)
�1 2�
5.P
(a m
ult
iple
of
4)�1 4�
6.P
(les
s th
an o
r eq
ual
to
8)�2 3�
7.P
(a f
acto
r of
12)
�1 2�8.
P(n
ot a
mu
ltip
le o
f 4)
�3 4�
9.P
(1,3
,or
11)
�1 4�10
.P
(a m
ult
iple
of
5)�1 6�
Th
e st
ud
ents
at
Job
’s h
igh
sch
ool
wer
e su
rvey
ed t
o d
eter
min
e th
eir
favo
rite
foo
ds.
Th
e re
sult
s ar
esh
own
in
th
e ta
ble
at
the
righ
t.S
up
pos
e st
ud
ents
wer
e ra
nd
omly
sele
cted
an
d a
sked
wh
at t
hei
rfa
vori
te f
ood
is.
Fin
d t
he
pro
bab
ilit
yof
eac
h e
ven
t.W
rite
as
a fr
acti
on i
nsi
mp
lest
for
m.
11.
P(s
teak
)�1 5�
12.
P(s
pagh
etti
)� 43 0�
13.
P(c
erea
l or
sea
food
)�1 8�
14.
P(n
ot c
how
mei
n)
�7 8�
15.
P(p
izza
)�1 49 0�
16.
P(c
erea
l or
ste
ak)
� 49 0�
17.
P(n
ot s
teak
)�4 5�
18.
P(n
ot c
erea
l or
sea
food
)�7 8�
19.
P(c
hic
ken
)0
20.
P(c
how
mei
n o
r sp
agh
etti
)�1 5�
Fav
orit
e F
ood
Res
pon
ses
pizz
a19
stea
k8
chow
mei
n5
seaf
ood
4sp
agh
etti
3ce
real
16SDAP3.3
Exer
cise
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Sim
ple
Eve
nts
Cha
pter
910
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-1
Wh
at i
s th
e p
rob
abil
ity
of r
olli
ng
a m
ult
iple
of
3 on
a n
um
ber
cu
be
mar
ked
wit
h 1
,2,3
,4,5
,an
d 6
on
its
fac
es.
P(m
ult
iple
of
3) �
��2 6�
Two
num
bers
are
mul
tiple
s of
3:3
and
6.
��1 3�
Sim
plify
.
Th
e pr
obab
ilit
y of
rol
lin
g a
mu
ltip
le o
f 3
is �1 3�
or a
bou
t 33
.3%
.
Wh
at i
s th
e p
rob
abil
ity
of n
otro
llin
g a
mu
ltip
le o
f 3
on a
nu
mb
ercu
be
mar
ked
wit
h 1
,2,3
,4,5
,an
d 6
on
its
fac
es?
P(A
) �
P(n
otA
) �
1
�1 3��
P(n
ot A
) �
1S
ubst
itute
�1 3�fo
r P
(A).
��1 3�
��1 3�
Sub
trac
t �1 3�
from
eac
h si
de�
��
��
��
�P
(not
A)
� �2 3�
Sim
plify
.
Th
e pr
obab
ilit
y of
not
roll
ing
a m
ult
iple
of
3 is
�2 3�or
abo
ut
66.7
%.
A s
et o
f 30
car
ds
is n
um
ber
ed 1
,2,3
,…,3
0.S
up
pos
e yo
u p
ick
a c
ard
at
ran
dom
wit
hou
t lo
okin
g.F
ind
th
e p
rob
abil
ity
of e
ach
eve
nt.
Wri
te a
sa
frac
tion
in
sim
ple
st f
orm
.
1.P
(12)
� 31 0�2.
P(2
or
3)� 11 5�
3.P
(odd
nu
mbe
r)�1 2�
4.P
(a m
ult
iple
of
5)�1 5�
5.P
(not
a m
ult
iple
of
5)�4 5�
6.P
(les
s th
an o
r eq
ual
to
10)
�1 3�
mu
ltip
les
of 3
pos
sibl
e�
��
tota
l n
um
bers
pos
sibl
e
The
pro
bab
ility
of a
sim
ple
even
t is
a r
atio
tha
t co
mpa
res
the
num
ber
of fa
vora
ble
outc
omes
to
the
num
ber
of p
ossi
ble
outc
omes
.Out
com
es o
ccur
at
ran
do
mif
each
out
com
e oc
curs
by
chan
ce.
Two
even
ts t
hat
are
the
only
one
s th
at c
an p
ossi
bly
happ
en a
re c
om
ple
men
tary
eve
nts
.The
sum
of
the
prob
abili
ties
of c
ompl
emen
tary
eve
nts
is 1
.
Exam
ple
1
Exam
ple
2
6SD
AP
3.3
Answers (Lesson 9-1)
Chapter 9 A2 Glencoe California Mathematics, Grade 6
An
swer
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Wor
d Pr
oble
m P
ract
ice
Sim
ple
Eve
nts
Cha
pter
913
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Lesson 9–1
pygp
9-1
CO
INS
Su
san
op
ened
her
pig
gy b
ank
an
d c
oun
ted
the
nu
mb
er o
f ea
ch c
oin
.Th
e ta
ble
at
the
righ
tsh
ows
the
resu
lts.
For
Exe
rcis
es 1
–3,a
ssu
me
that
the
coin
s ar
e p
ut
in a
bag
an
d o
ne
is c
hos
en a
tra
nd
om.
1.W
hat
is
the
prob
abil
ity
that
a q
uar
ter
is c
hos
en?
�1 6�
2.W
hat
is
the
prob
abil
ity
that
a n
icke
l or
a di
me
is c
hos
en?
�4 93 0�
3.W
hat
is
the
prob
abil
ity
that
th
e ch
osen
coin
is
wor
th m
ore
than
5 c
ents
?
�2 5�
4.N
UM
BER
CU
BES
Juan
has
tw
o n
um
ber
cube
s,ea
ch w
ith
fac
es n
um
bere
d 1,
2,…
6.W
hat
is
the
prob
abil
ity
that
he
can
rol
l th
e cu
bes
so t
hat
th
e su
m o
fth
e fa
ces
show
ing
equ
als
11?
� 11 8�
5.SK
ATE
BO
AR
DS
Car
lott
a bo
ugh
t a
new
skat
eboa
rd f
or w
hic
h t
he
prob
abil
ity
ofh
avin
g a
defe
ctiv
e w
hee
l is
0.0
15.W
hat
is t
he
prob
abil
ity
of n
ot h
avin
g a
defe
ctiv
e w
hee
l?0.
985
6.C
ALC
ULA
TOR
SJa
ke’s
tea
cher
had
6ca
lcu
lato
rs f
or 2
8 st
ude
nts
to
use
.If
the
firs
t st
ude
nts
to
use
th
e ca
lcu
lato
rs a
rech
osen
at
ran
dom
,wh
at i
s th
epr
obab
ilit
y th
at J
ake
wil
l ge
t on
e?
� 13 4�
7.V
EHIC
LES
Th
e re
nta
l ca
r co
mpa
ny
had
14 s
edan
s an
d 8
min
ivan
s av
aila
ble
tore
nt.
If t
he
nex
t cu
stom
er p
icks
ave
hic
le a
t ra
ndo
m,w
hat
is
the
prob
abil
ity
that
a m
iniv
an i
s ch
osen
?
� 14 1�
8.M
USI
CT
ina
has
16
pop
CD
s,6
clas
sica
l,an
d 2
rock
.Tin
a ch
oose
s a
CD
at
ran
dom
.Wh
at i
s th
e pr
obab
ilit
ysh
e do
es n
ot c
hoo
se a
cla
ssic
al C
D?
�3 4�
Coi
nN
um
ber
quar
ters
15
dim
es21
nic
kels
22
pen
nie
s32
6SD
AP
3.3
A s
et o
f ca
rds
is n
um
ber
ed 1
,2,3
,… 2
4.S
up
pos
e yo
u p
ick
a c
ard
at
ran
dom
wit
hou
t lo
okin
g.F
ind
th
e p
rob
abil
ity
of e
ach
eve
nt.
Wri
te a
sa
frac
tion
in
sim
ple
st f
orm
.
1.P
(5)
2.P
(mu
ltip
le o
f 4)
3.P
(6 o
r 17
)
� 21 4��1 4�
� 11 2�
4.P
(not
equ
al t
o 15
)5.
P(n
ot a
fac
tor
of 6
)6.
P(o
dd n
um
ber)
�2 23 4��5 6�
�1 2�
CO
MM
UN
ITY
SER
VIC
ET
he
tab
le s
how
s th
e st
ud
ents
in
volv
ed i
nco
mm
un
ity
serv
ice.
Su
pp
ose
one
stu
den
t is
ran
dom
ly s
elec
ted
to
rep
rese
nt
the
sch
ool
at a
sta
te-w
ide
awar
ds
cere
mon
y.F
ind
th
ep
rob
abil
ity
of e
ach
eve
nt.
Wri
te a
s a
frac
tion
in
sim
ple
st f
orm
.
7.P
(boy
)�5 8�
8.P
(not
6th
gra
der)
�1 2�
9.P
(gir
l)
�3 8�10
.P
(8th
gra
der)
� 13 0�
11.
P(b
oy o
r gi
rl)
112
.P
(6th
or
7th
gra
der)
� 17 0�
13.
P(7
th g
rade
r)�1 5�
14.
P(n
ot a
9th
gra
der)
1
MEN
UA
del
icat
esse
n s
erve
s d
iffe
ren
t m
enu
ite
ms,
of w
hic
h 2
are
sou
ps,
6 ar
e sa
nd
wic
hes
,an
d 4
are
sal
ads.
How
lik
ely
is i
t fo
r ea
chev
ent
to h
app
en i
f yo
u c
hoo
se o
ne
item
at
ran
dom
fro
m t
he
men
u?
Exp
lain
you
r re
ason
ing.
15.
P(s
andw
ich
)�1 2�
16.
P(n
ot a
sou
p)�5 6�
17.
P(s
alad
)�1 3�
Th
ere
are
6 sa
nd
wic
h
Th
ere
are
2 so
up
T
her
e ar
e 4
sala
d
item
s o
f th
e 12
men
uit
ems.
So
th
ere
item
s o
f th
e 12
men
uit
ems.
are
10 n
on
-so
up
item
s.it
ems
of
the
12 m
enu
item
s.� 16 2�
��1 2�
�1 10 2��
�5 6�� 14 2�
��1 3�
18.
NU
MB
ER C
UB
EW
hat
is
the
prob
abil
ity
of r
olli
ng
an e
ven
nu
mbe
r or
a p
rim
e n
um
ber
on a
nu
mbe
r cu
be?
Wri
te a
s a
frac
tion
in
sim
ples
t fo
rm.
�5 6�
19.
CLO
SIN
G T
IME
At
a co
nve
nie
nce
sto
re t
her
e is
a 2
5% c
han
ce a
cu
stom
eren
ters
th
e st
ore
wit
hin
on
e m
inu
te o
f cl
osin
g ti
me.
Des
crib
e th
eco
mpl
emen
tary
eve
nt
and
fin
d it
s pr
obab
ilit
y.T
her
e is
a 7
5% c
han
cen
o c
ust
om
er w
ill e
nte
r w
ith
in o
ne
min
ute
of
clo
sin
g t
ime.
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Prac
tice
Sim
ple
Eve
nts
Cha
pter
912
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-1
Com
mu
nit
y S
ervi
cegi
rls
15bo
ys25
6th
gra
ders
207t
h g
rade
rs8
8th
gra
ders
12
6SD
AP
3.3
Answers (Lesson 9-1)
Chapter 9 A3 Glencoe California Mathematics, Grade 6
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Less
on R
eadi
ng G
uide
S
amp
le S
pac
es
Cha
pter
915
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Lesson 9–2
pygp
9-2
Get
Rea
dy
for
the
Less
on
Com
ple
te t
he
Min
i L
ab a
t th
e to
p o
f p
age
465
in y
our
text
boo
k.W
rite
you
r an
swer
s b
elow
.
1.B
efor
e yo
u p
lay,
mak
e a
con
ject
ure
.Do
you
th
ink
that
eac
h p
laye
r h
as a
neq
ual
ch
ance
of
win
nin
g? E
xpla
in.
See
stu
den
ts’w
ork
.
2.N
ow,p
lay
the
gam
e.W
ho
won
? W
hat
was
th
e fi
nal
sco
re?
No
te:
Aft
er 2
0 to
sses
,th
e g
ames
may
be
tied
.Th
e n
um
ber
of
win
s fo
r ea
ch p
laye
r w
ill b
e ab
ou
t th
e sa
me.
Rea
d t
he
Less
on
3.H
ow d
oes
a tr
ee d
iagr
am r
esem
ble
a tr
ee?
Sam
ple
an
swer
:It
sta
rts
wit
h a
bas
e fo
r ea
ch e
ven
t (t
he
firs
t it
em o
n t
he
left
) an
d t
hen
bra
nch
es o
ut
to s
ho
w t
he
po
ssib
le o
utc
om
es f
or
the
even
t.4.
How
can
you
use
a t
able
to
fin
d th
e n
um
ber
of p
ossi
ble
outc
omes
of
anev
ent?
Sam
ple
an
swer
:C
ou
nt
the
nu
mb
er o
f en
trie
s lis
ted
inth
e tr
ee in
th
e sa
mp
le s
pac
e.5.
How
do
you
kn
ow t
he
gam
e pl
ayed
in
Exa
mpl
e 3
is f
air?
Sam
ple
answ
er:
Of
the
fou
r p
oss
ible
ou
tco
mes
,tw
o f
avo
r ea
ch p
laye
r.T
her
efo
re,t
he
pro
bab
ility
th
at e
ach
pla
yer
can
win
is 5
0%.
Rem
emb
er W
hat
Yo
u L
earn
ed6.
Dra
w a
tre
e di
agra
m t
hat
sh
ows
a fa
ir g
ame
that
is
diff
eren
t fr
om
the
exam
ples
in
you
r te
xtbo
ok.C
an y
ou t
hin
k of
a w
ay t
o dr
aw a
tr
ee d
iagr
am t
hat
sh
ows
a ga
me
that
is
not
fair
? M
ake
sure
you
in
clu
de a
des
crip
tion
if
the
gam
e is
not
cle
ar f
rom
you
r di
agra
m.
Sam
ple
an
swer
:Fa
ir g
ame:
Pla
yer
1 to
sses
a
coin
tw
ice.
Pla
yer
2 to
sses
a
coin
tw
ice.
Th
e p
laye
r th
at
get
s ta
ils t
he
mo
st w
ins.
Un
fair
gam
e:A
be,
Bet
ty,a
nd
C
arl e
ach
to
ss a
co
in.T
he
pla
yer
that
get
s ta
ils t
he
mo
st a
fter
3 t
oss
es w
ins.
Th
e p
laye
r w
ho
se n
ame
beg
ins
wit
h a
vo
wel
get
s o
nly
2 t
oss
es.
Toss
Third
Toss
Seco
ndTo
ssFi
rst
Spac
eSa
mpl
e
H TH
Abe
T
H H
H T
H T
T H
T T
H TH T
H T H T
H T
H T H T
H T
H
H H
TH
H H
H T
T
T H
HT
H T
T T
HT
T T
H TH T
H T H T
H T
H T H T
H H
HH
H T
H T
HH
T T
T H
HT
H T
T T
HT
T T
Betty
Carl
Unfa
ir Ga
me
6SD
AP
3.1
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Enri
chm
ent
Cha
pter
914
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-1
Co
in-T
oss
ing
Exp
erim
ents
If a
coi
n i
s to
ssed
3 t
imes
,th
ere
are
8 po
ssib
le o
utc
omes
.Th
ey a
re l
iste
d in
th
eta
ble
belo
w.
On
ce a
ll t
he
outc
omes
are
kn
own
,th
e pr
obab
ilit
y of
an
y ev
ent
can
be
fou
nd.
For
exa
mpl
e,th
e pr
obab
ilit
y of
get
tin
g 2
hea
ds i
s �3 8�.
Not
ice
that
th
is i
s th
esa
me
as g
etti
ng
1 ta
il.
1.A
coi
n i
s to
ssed
4 t
imes
.Com
plet
e th
is c
har
t to
sh
ow t
he
poss
ible
outc
omes
.
2.W
hat
is
the
prob
abil
ity
of g
etti
ng
all
tail
s?� 11 6�
3.N
ow c
ompl
ete
this
tab
le.M
ake
char
ts l
ike
the
one
in E
xerc
ise
1 to
hel
pfi
nd
the
answ
ers.
Loo
k fo
r pa
tter
ns
in t
he
nu
mbe
rs.
4.W
hat
hap
pen
s to
th
e n
um
ber
of o
utc
omes
? th
e pr
obab
ilit
y of
all
tai
ls?
Sam
ple
an
swer
:It
is d
ou
blin
g;
it is
hal
vin
g.
Nu
mb
er o
f H
ead
s0
12
3
Ou
tcom
esT
TT
HT
TH
HT
HH
H
TH
TT
HH
TT
HH
TH
Nu
mb
er o
f H
ead
s0
12
3
Ou
tcom
esT
TT
TH
TT
TH
HT
TT
HH
H
TH
TT
HT
HT
HT
HH
TT
HT
TH
HT
HH
TH
HH
HH
4
TT
TH
TT
HH
HH
HT
TH
TH
HT
TH
Nu
mb
er o
f C
oin
Tos
ses
23
45
67
8
Tot
al O
utc
omes
48
1632
6412
825
6
Pro
bab
ilit
y of
Get
tin
g A
llT
ails
�1 4��1 8�
� 11 6�� 31 2�
� 61 4�� 11 28�
� 21 56�
6SD
AP
3.1
Answers (Lessons 9-1 and 9-2)
Chapter 9 A4 Glencoe California Mathematics, Grade 6
An
swer
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Skill
s Pr
actic
eS
amp
le S
pac
es
Cha
pter
917
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Lesson 9–2
pygp
9-2
Th
e sp
inn
er a
t th
e ri
ght
is s
pu
n t
wic
e.
1.D
raw
a t
ree
diag
ram
to
repr
esen
t th
e si
tuat
ion
.
2.W
hat
is
the
prob
abil
ity
of g
etti
ng
at
leas
t on
e A
?�5 9�
For
eac
h s
itu
atio
n,m
ake
a tr
ee d
iagr
am o
r ta
ble
to
show
th
esa
mp
le s
pac
e.T
hen
giv
e th
e to
tal
nu
mb
er o
f ou
tcom
es.
3.ch
oosi
ng
a h
ambu
rger
or
hot
dog
an
d po
tato
sal
ad o
r m
acar
oni
sala
d
Th
ere
are
4 p
oss
ible
ou
tco
mes
.
4.ch
oosi
ng
a vo
wel
fro
m t
he
wor
d C
OM
PU
TE
R
and
a co
nso
nan
t fr
om t
he
wor
d B
OO
K
Th
ere
are
6 p
oss
ible
o
utc
om
es.
5.ch
oosi
ng
betw
een
th
e n
um
bers
1,2
or
3,an
d th
e co
lors
blu
e,re
d,or
gre
en
Th
ere
are
9 p
oss
ible
o
utc
om
es.
blu
e
gre
en
red
1, g
reen
Num
ber
Sam
ple
Sp
ace
1, b
lue
1, r
ed
21 3
Co
lor
blu
e
gre
en
red
2, g
reen
2, b
lue
2, r
ed
blu
e
gre
en
red
3, g
reen
3, b
lue
3, r
ed
OB K
OK
OB
UB K
UK
UB
EB K
EK
EB
Vow
el f
rom
CO
MP
UT
ER
Co
nso
nan
tfr
om
BO
OK
Sam
ple
Sp
ace
ham
bur
ger
po
tato
mac
aro
niha
mb
urg
er, m
acar
oni
sal
ad
Ent
ree
Sal
adS
amp
le S
pac
e
ho
t d
og
po
tato
mac
aro
ni
hot
do
g, p
ota
to s
alad
ham
bur
ger
, po
tato
sal
ad
hot
do
g, m
acar
oni
sal
ad
A
A CB
A C
Sam
ple
Sp
ace
2nd
spin
1st
spin
A A
A B
B
A CB
B C
B A
B B
C
A CB
C C
C A
C B
B
CA
6SD
AP
3.1
Exer
cise
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Sam
ple
Sp
aces
Cha
pter
916
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-2
WA
TCH
ESA
cer
tain
typ
e of
wat
ch c
omes
in
bro
wn
or
bla
ck a
nd
in
asm
all
or l
arge
siz
e.F
ind
th
e n
um
ber
of
colo
r-si
ze c
omb
inat
ion
s th
atar
e p
ossi
ble
.
Mak
e a
tabl
e to
sh
ow t
he
sam
ple
spac
e.T
hen
giv
e th
e to
tal
nu
mbe
r of
ou
tcom
es.
Th
ere
are
fou
r di
ffer
ent
colo
r an
d si
ze c
ombi
nat
ion
s.
CH
ILD
REN
Th
e ch
ance
of
hav
ing
eith
er a
boy
or
a gi
rl i
s 50
%.W
hat
is
the
pro
bab
ilit
y of
th
e S
mit
hs
hav
ing
two
girl
s?
Mak
e a
tree
dia
gram
to
show
th
e sa
mpl
e sp
ace.
Th
en f
ind
the
prob
abil
ity
of h
avin
g tw
o gi
rls.
Th
e sa
mpl
e sp
ace
con
tain
s 4
poss
ible
ou
tcom
es.O
nly
1 o
utc
ome
has
bot
h c
hil
dren
bei
ng
girl
s.S
o,th
e pr
obab
ilit
y of
hav
ing
two
girl
s is
�1 4�.
For
eac
h s
itu
atio
n,m
ake
a tr
ee d
iagr
am o
r ta
ble
to
show
th
e sa
mp
lesp
ace.
Th
en g
ive
the
tota
l n
um
ber
of
outc
omes
.
1.ch
oosi
ng
an o
utf
it f
rom
a g
reen
sh
irt,
blu
e sh
irt,
or a
red
sh
irt,
and
blac
kpa
nts
or
blu
e pa
nts
See
stu
den
ts’w
ork
.Th
ere
are
6 o
utc
om
es.
2.ch
oosi
ng
a vo
wel
fro
m t
he
wor
d C
OU
NT
ING
an
d a
con
son
ant
from
th
ew
ord
PR
IME
See
stu
den
ts’w
ork
.Th
ere
are
9 o
utc
om
es.
bo
yb
oy
gir
lb
oy,
gir
l
Ch
ild
1C
hil
d 2
Sam
ple
Sp
ace
gir
lb
oy
gir
l
gir
l, b
oy
bo
y, b
oy
gir
l, g
irl
A g
ame
in w
hich
pla
yers
of
equa
l ski
ll ha
ve a
n eq
ual c
hanc
e of
win
ning
is a
fai
r g
ame.
A t
ree
dia
gra
mor
tab
le is
use
d to
sho
w a
ll of
the
pos
sibl
e ou
tcom
es,
or s
amp
le s
pac
e, in
a p
roba
bilit
yex
perim
ent.
Col
orS
ize
Bro
wn
Sm
all
Bro
wn
Lar
ge
Bla
ckS
mal
l
Bla
ckL
arge
Exam
ple
1
Exam
ple
2
6SD
AP
3.1
Answers (Lesson 9-2)
Chapter 9 A5 Glencoe California Mathematics, Grade 6
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Wor
d Pr
oble
m P
ract
ice
Sam
ple
Sp
aces
Cha
pter
919
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Lesson 9–2
pygp
9-2
1.G
ASO
LIN
EC
raig
sto
ps a
t a
gas
stat
ion
to f
ill
his
gas
tan
k.H
e m
ust
ch
oose
betw
een
fu
ll-s
ervi
ce o
r se
lf-s
ervi
ce a
nd
betw
een
reg
ula
r,m
idgr
ade,
and
prem
ium
gas
olin
e.D
raw
a t
ree
diag
ram
or
tabl
e sh
owin
g th
e po
ssib
leco
mbi
nat
ion
s of
ser
vice
an
d ga
soli
ne
type
.How
man
y po
ssib
le c
ombi
nat
ion
sar
e th
ere?
Th
ere
are
6 p
oss
ible
com
bin
atio
ns.
reg
ular
pre
miu
m
mid
gra
de
full,
pre
miu
m
Ser
vice
Sam
ple
Sp
ace
full,
reg
ular
full,
mid
gra
de
Sel
f
Ful
l
reg
ular
pre
miu
m
mid
gra
de
self,
pre
miu
m
self,
reg
ular
self,
mid
gra
de
Gas
olin
e
3.C
OIN
SIn
Exe
rcis
e 2,
wh
at i
s th
epr
obab
ilit
y of
get
tin
g 2
hea
ds,t
hen
2
tail
s?
� 11 6�
4.EQ
UIP
MEN
TT
he
com
pute
r ac
cess
ory
that
Joa
nn
e is
con
side
rin
g se
llin
g at
her
sto
re c
omes
in
wh
ite,
beig
e,gr
ay,
orbl
ack
and
as a
n o
ptic
al m
ouse
,m
ech
anic
al m
ouse
,or
trac
kbal
l.H
owm
any
com
bin
atio
ns
of c
olor
an
d m
odel
mu
st s
he
stoc
k in
ord
er t
o h
ave
at l
east
one
of e
very
pos
sibl
e co
mbi
nat
ion
?12
2.C
OIN
SJu
dy t
osse
s a
coin
4 t
imes
.Dra
wa
tree
dia
gram
or
tabl
e sh
owin
g th
epo
ssib
le o
utc
omes
.Wh
at i
s th
epr
obab
ilit
y of
get
tin
g at
lea
st 2
tai
ls? �1 11 6�
Four
thTo
ssT
hird
Toss
Sec
ond
Toss
Firs
tTo
ssS
pac
eS
amp
le
H TH T
H T H T
H T
H T H T
H H
T H
H H
H T
H H
H H
H H
T T
H T
H H
H T
H T
H T
T H
H T
T T
H TH T
H T H T
H T
H T H T
T H
H H
T H
H T
T H
T H
T H
T T
T T
H H
T T
H T
T T
T H
T T
T T
H T
6SD
AP
3.1
For
eac
h s
itu
atio
n,f
ind
th
e sa
mp
le s
pac
e u
sin
g a
tab
le o
r tr
eed
iagr
am.
1.ch
oosi
ng
blu
e,gr
een
,or
yell
ow w
all
pain
t w
ith
wh
ite,
beig
e,or
gra
ycu
rtai
ns
2.ch
oosi
ng
a lu
nch
con
sist
ing
of a
sou
p,sa
lad,
and
san
dwic
h f
rom
th
e m
enu
sh
own
in
th
e ta
ble.
3.G
AM
EK
imik
o an
d M
iko
are
play
ing
a ga
me
in w
hic
h e
ach
gir
l ro
lls
an
um
ber
cube
.If
the
sum
of
the
nu
mbe
rs i
s a
prim
e n
um
ber,
then
Mik
ow
ins.
Oth
erw
ise
Kim
iko
win
s.F
ind
the
sam
ple
spac
e.T
hen
det
erm
ine
wh
eth
er t
he
gam
e is
fai
r.
P(K
imik
o)�
�� 17 2�
;P
(Mik
o)
��
� 15 2�
Th
e g
ame
is n
ot
fair
sin
ce t
he
pro
bab
iliti
es a
re u
neq
ual
.
1 �
2 �
4 �
6 �
2�
��
363
�5
� 5
� 4
� 3
� 1
��
�36
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Prac
tice
Sam
ple
Sp
aces
Cha
pter
918
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-2 S
oup
Sal
adS
and
wic
hT
orte
llin
iC
aesa
rR
oast
Bee
fL
enti
lM
acar
oni
Ham
Tu
rkey
Tort
ellin
iC
aesa
rR
oas
t B
eef
Tort
ellin
iC
aesa
rH
amTo
rtel
lini
Cae
sar
Turk
eyTo
rtel
lini
Mac
aro
ni
Ro
ast
Bee
fTo
rtel
lini
Mac
aro
ni
Ham
Tort
ellin
iM
acar
on
iTu
rkey
Len
til
Cae
sar
Ro
ast
Bee
fL
enti
lC
aesa
rH
amL
enti
lC
aesa
rTu
rkey
Len
til
Mac
aro
ni
Ro
ast
Bee
fL
enti
lM
acar
on
iH
amL
enti
lM
acar
on
iTu
rkey
sam
ple
an
swer
:
Sum
�2
Sum
�3
Sum
�4
Sum
�5
Sum
�6
Sum
�7
Sum
�8
Sum
�9
Sum
�10
Sum
�11
Sum
�12
1 �
1 =
22
�1
= 3
1 �
2 =
3
1 �
3 =
42
�2
= 4
3 �
1 =
4
1 �
4 =
52
�3
= 5
3 �
2 =
54
�1
= 5
1 �
5 =
62
�4
= 6
3 �
3 =
64
�2
= 6
5 �
1 =
6
1 �
6 =
72
�5
= 7
3 �
4 =
74
�3
= 7
5 �
2 =
76
�1
= 7
2 �
6 =
83
�5
= 8
4 �
4 =
85
�3
= 8
6 �
2 =
8
3 �
6 =
94
�5
= 9
5 �
4 =
96
�3
= 9
4�
6=
105
�5
=10
6+
4=
10
5�
6=
116
�5
=11
6�
6�
12
blu
e
blu
e p
aint
, whi
te c
urta
ins
blu
e p
aint
, bei
ge
curt
ains
blu
e p
aint
, gra
y cu
rtai
ns
whi
te
bei
ge
gra
y
gre
en p
aint
, whi
te c
urta
ins
gre
en p
aint
, bei
ge
curt
ains
gre
en p
aint
, gra
y cu
rtai
ns
whi
te
bei
ge
gra
y
yello
w p
aint
, whi
te c
urta
ins
yello
w p
aint
, bei
ge
curt
ains
yello
w p
aint
, gra
y cu
rtai
ns
whi
te
bei
ge
gra
y
gre
en
yello
w
Pai
ntS
amp
le S
pac
eC
urta
ins
6SD
AP
3.1
Answers (Lesson 9-2)
Chapter 9 A6 Glencoe California Mathematics, Grade 6
An
swer
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
921
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Lesson 9–3
pygp
9-3
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n a
t th
e to
p o
f p
age
471
in y
our
text
boo
k.W
rite
you
r an
swer
s b
elow
.
1.A
ccor
din
g to
th
e ta
ble,
how
man
y si
zes
of ju
nio
rs’ j
ean
s ar
e th
ere?
7
2.H
ow m
any
len
gth
s ar
e th
ere?
3
3.F
ind
the
prod
uct
of
the
two
nu
mbe
rs y
ou f
oun
d in
Exe
rcis
es 1
an
d 2.
21
4.D
raw
a t
ree
diag
ram
to
hel
p yo
u f
ind
the
nu
mbe
r of
dif
fere
nt
size
an
d le
ngt
h
com
bin
atio
ns.
How
doe
s th
e n
um
ber
of
outc
omes
com
pare
to
the
prod
uct
you
fo
un
d ab
ove?
Sam
ple
an
swer
:Th
ere
are
21 d
iffe
ren
t si
zes
and
len
gth
s o
f ju
nio
rs’j
ean
s.T
his
is t
he
sam
e as
th
e p
rod
uct
fo
un
d a
bov
e.
Rea
d t
he
Less
on
5.W
hat
ope
rati
on i
s u
sed
in t
he
Fu
nda
men
tal
Cou
nti
ng
Pri
nci
ple?
mu
ltip
licat
ion
6.H
ow i
s th
e in
form
atio
n i
n a
tre
e di
agra
m
or t
able
dif
fere
nt
from
th
e in
form
atio
n
prov
ided
by
cou
nti
ng?
Sam
ple
an
swer
:T
he
tree
dia
gra
m,i
n a
dd
itio
n t
oin
dic
atin
g t
he
tota
l nu
mb
er o
f p
oss
ible
o
utc
om
es,a
lso
list
s th
e o
utc
om
es
so t
hat
yo
u c
an s
ee t
he
con
ten
t o
f th
e o
utc
om
es a
s w
ell a
s th
eir
nu
mb
er.
Rem
emb
er W
hat
Yo
u L
earn
ed7.
Wri
te t
he
Fu
nda
men
tal
Cou
nti
ng
Pri
nci
ple
in y
our
own
wor
ds.
Sam
ple
an
swer
:If
eve
nt
Mca
n o
ccu
r in
mw
ays
and
isfo
llow
ed b
y ev
ent
Nth
at c
an o
ccu
r in
nw
ays,
then
th
e ev
ent
Mfo
llow
ed b
y N
can
occ
ur
in m
�n
way
s.
pet
ite
tall
reg
ular
3 ta
ll
Siz
esS
amp
le S
pac
e 3
pet
ite
3 re
gul
ar3
Leng
ths
pet
ite
tall
reg
ular
5 ta
ll
5 p
etite
5 re
gul
ar5
pet
ite
tall
reg
ular
7 ta
ll
7 p
etite
7 re
gul
ar7
pet
ite
tall
reg
ular
9 ta
ll
9 p
etite
9 re
gul
ar9
pet
ite
tall
reg
ular
11 t
all
11 p
etite
11 r
egul
ar11
pet
ite
tall
reg
ular
13 t
all
13 p
etite
13 r
egul
ar13
pet
ite
tall
reg
ular
15 t
all
15 p
etite
15 r
egul
ar15
6SD
AP
3.1
Less
on R
eadi
ng G
uide
Th
e F
un
dam
enta
l Co
un
tin
g P
rin
cip
le
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Enri
chm
ent
Cha
pter
920
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-2
Pro
bab
iliti
es a
nd
Reg
ion
sT
he
spin
ner
at
the
righ
t ca
n b
e u
sed
to i
ndi
cate
th
at t
he
prob
abil
ity
of
lan
din
g in
eit
her
of
two
regi
ons
is �1 2�.
P(A
) �
�1 2�P
(B)
� �1 2�
Rea
d t
he
des
crip
tion
of
each
sp
inn
er.U
sin
g a
pro
trac
tor
and
ru
ler,
div
ide
each
sp
inn
er i
nto
reg
ion
s th
at s
how
th
e in
dic
ated
pro
bab
ilit
y.
1.T
wo
regi
ons
A a
nd
B:t
he
prob
abil
ity
of l
andi
ng
in r
egio
n A
is
�3 4�.
Wh
at i
s th
e pr
obab
ilit
y of
lan
din
g in
reg
ion
B?
P(B
) �
�1 4�
2.T
hre
e re
gion
s A
,B,a
nd
C:t
he
prob
abil
ity
of l
andi
ng
in r
egio
n A
is �1 2�
and
the
prob
abil
ity
of l
andi
ng
in r
egio
n B
is
�1 4�.W
hat
is
the
prob
abil
ity
of l
andi
ng
in r
egio
n C
?
P(C
) �
�1 4�
3.T
hre
e re
gion
s A
,B,a
nd
C:t
he
prob
abil
ity
of l
andi
ng
in r
egio
n A
is �3 8�
and
the
prob
abil
ity
of l
andi
ng
in r
egio
n B
is
�1 8�.W
hat
is
the
prob
abil
ity
of l
andi
ng
in r
egio
n C
?
P(C
) �
�1 2�
4.F
our
regi
ons
A,B
,C,a
nd
D:t
he
prob
abil
ity
of l
andi
ng
in r
egio
n A
is � 11 6�
,th
e pr
obab
ilit
y of
lan
din
g in
reg
ion
B i
s �1 8�,
and
the
prob
abil
ity
of l
andi
ng
in r
egio
n C
is
�1 4�.W
hat
is
the
prob
abil
ity
of l
andi
ng
in
regi
on D
?
P(D
) �
� 19 6�
5.T
he
spin
ner
at
the
righ
t is
an
equ
ilat
eral
tri
angl
e,di
vide
d in
to
regi
ons
by l
ine
segm
ents
th
at d
ivid
e th
e si
des
in h
alf.
Is t
he
spin
ner
div
ided
in
to r
egio
ns
of e
qual
pro
babi
lity
?ye
s
BCD
A
BC
A
C
A
BB
A
A
B
6SDAP3.1
Answers (Lessons 9-2 and 9-3)
Chapter 9 A7 Glencoe California Mathematics, Grade 6
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
923
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Lesson 9–3
pygp
9-3
Use
th
e F
un
dam
enta
l C
oun
tin
g P
rin
cip
le t
o fi
nd
th
e to
tal
nu
mb
er o
fou
tcom
es i
n e
ach
sit
uat
ion
.
1.ro
llin
g tw
o n
um
ber
cube
s an
d to
ssin
g on
e co
in72
2.ch
oosi
ng
rye
or B
erm
uda
gra
ss a
nd
3 di
ffer
ent
mix
ture
s of
fer
tili
zer
6
3.m
akin
g a
san
dwic
h w
ith
ham
,tu
rkey
,or
roas
t be
ef;S
wis
s or
pro
volo
ne
chee
se;a
nd
mu
star
d or
may
onai
se12
4.to
ssin
g 4
coin
s16
5.ch
oosi
ng
from
3 s
izes
of
dist
ille
d,fi
lter
ed,o
r sp
rin
g w
ater
9
6.ch
oosi
ng
from
3 f
lavo
rs o
f ju
ice
and
3 si
zes
9
7.ch
oosi
ng
from
35
flav
ors
of i
ce c
ream
;on
e,tw
o,or
th
ree
scoo
ps;a
nd
suga
ror
waf
fle
con
e21
0
8.pi
ckin
g a
day
of t
he
wee
k an
d a
date
in
th
e m
onth
of A
pril
210
9.ro
llin
g 3
nu
mbe
r cu
bes
and
toss
ing
2 co
ins
864
10.
choo
sin
g a
4-le
tter
pas
swor
d u
sin
g on
ly v
owel
s62
5
11.
choo
sin
g a
bicy
cle
wit
h o
r w
ith
out
shoc
k ab
sorb
ers;
wit
h o
r w
ith
out
ligh
ts;a
nd
5 co
lor
choi
ces
20
12.
a li
cen
se p
late
th
at h
as 3
nu
mbe
rs f
rom
0 t
o 9
and
2 le
tter
s67
6,00
06SD
AP
3.1
Skill
s Pr
actic
e T
he
Fu
nd
amen
tal C
ou
nti
ng
Pri
nci
ple
Exer
cise
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
922
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-3
CLO
THIN
GA
nd
y h
as 5
sh
irts
,3 p
airs
of
pan
ts,a
nd
6 p
airs
of
sock
s.H
ow m
any
dif
fere
nt
outf
its
can
An
dy
choo
se w
ith
a s
hir
t,p
air
ofp
ants
,an
d p
air
of s
ock
s?
An
dy c
an c
hoo
se 9
0 di
ffer
ent
outf
its.
Use
th
e F
un
dam
enta
l C
oun
tin
g P
rin
cip
le t
o fi
nd
th
e to
tal
nu
mb
er o
fou
tcom
es i
n e
ach
sit
uat
ion
.
1.ro
llin
g tw
o n
um
ber
cube
s36
2.to
ssin
g 3
coin
s8
3.pi
ckin
g on
e co
nso
nan
t an
d on
e vo
wel
105
4.ch
oosi
ng
one
of 3
pro
cess
or s
peed
s,2
size
s of
mem
ory,
and
4 si
zes
of
har
d dr
ive
24
5.ch
oosi
ng
a 4-
,6-,
or 8
-cyl
inde
r en
gin
e an
d 2-
or
4-w
hee
l dr
ive
6
6.ro
llin
g 2
nu
mbe
r cu
bes
and
toss
ing
2 co
ins
144
7.ch
oosi
ng
a co
lor
from
4 c
olor
s an
d a
nu
mbe
r fr
om 4
to
1028
If ev
ent
Mca
n oc
cur
in m
way
s an
d is
follo
wed
by
even
t N
that
can
occ
ur in
nw
ays,
the
n th
e ev
ent
Mfo
llow
ed b
y N
can
occu
r in
m�
nw
ays.
Thi
s is
cal
led
the
Fu
nd
amen
tal C
ou
nti
ng
Pri
nci
ple
.
num
ber
of s
hirt
snu
mbe
r of
pan
tsnu
mbe
r of
soc
ksto
tal n
umbe
r of
out
fits
�
�
�
�
5�
3�
6�
90
Exam
ple
1
6SD
AP
3.1
Stud
y Gu
ide
and
Inte
rven
tion
Th
e F
un
dam
enta
l Co
un
tin
g P
rin
cip
le
Answers (Lesson 9-3)
Chapter 9 A8 Glencoe California Mathematics, Grade 6
An
swer
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
925
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Lesson 9–3
pygp
9-3
1.SU
RFB
OA
RD
Jay
own
s 3
surf
boar
ds a
nd
2 w
etsu
its.
If h
e ta
kes
one
surf
boar
dan
d on
e w
etsu
it t
o th
e be
ach
,how
man
y di
ffer
ent
com
bin
atio
ns
can
he
choo
se?
6
2.SH
OPP
ING
Joh
n i
s tr
yin
g to
dec
ide
wh
ich
bag
of
dog
food
to
buy.
Th
e br
and
he
wan
ts c
omes
in
4 f
lavo
rs a
nd
3 si
zes.
How
man
y ch
oice
s ar
e th
ere?
12
3.LO
TTER
YT
o pu
rch
ase
a lo
tter
y ti
cket
,yo
u m
ust
sel
ect
4 n
um
bers
fro
m 0
to
9.H
ow m
any
poss
ible
lot
tery
tic
kets
can
be c
hos
en?
10,0
00
4.R
ESTA
UR
AN
TSM
iria
m’s
fav
orit
ere
stau
ran
t h
as 3
spe
cial
s ev
ery
day.
Eac
h s
peci
al h
as 2
ch
oice
s of
veg
etab
lean
d 3
choi
ces
of d
esse
rt.H
ow m
any
diff
eren
t m
eals
cou
ld M
iria
m h
ave?
18
5.R
OU
TES
Wh
en S
un
il g
oes
to t
he
buil
din
g w
her
e h
e w
orks
,he
can
go
thro
ugh
4 d
iffe
ren
t do
ors
into
th
e lo
bby.
Th
en h
e ca
n g
o to
th
e se
ven
th f
loor
by
taki
ng
2 di
ffer
ent
elev
ator
s or
2di
ffer
ent
stai
rway
s.H
ow m
any
diff
eren
t w
ays
can
Su
nil
get
fro
mou
tsid
e th
e bu
ildi
ng
to t
he
seve
nth
floo
r?16
6.ST
EREO
SJa
ilin
wen
t to
her
loc
al s
tere
ost
ore.
Giv
en h
er b
udg
et a
nd
the
avai
labl
e se
lect
ion
,sh
e ca
n c
hoo
sebe
twee
n 2
CD
pla
yers
,5 a
mpl
ifie
rs,
and
3 pa
irs
of s
peak
ers.
How
man
ydi
ffer
ent
ster
eos
can
Jai
lin
pu
rch
ase?
30
7.D
ESSE
RT
For
des
sert
you
can
ch
oose
appl
e,ch
erry
,blu
eber
ry,o
r pe
ach
pie
to
eat,
and
mil
k or
juic
e to
dri
nk.
How
man
y di
ffer
ent
com
bin
atio
ns
can
you
choo
se f
rom
?8
8.TE
STS
Joh
n i
s ta
kin
g a
tru
e or
fal
sequ
iz.T
her
e ar
e si
x qu
esti
ons
on t
he
quiz
.How
man
y w
ays
can
th
e qu
iz b
ean
swer
ed?
64
6SD
AP
3.1
Wor
d Pr
oble
m P
ract
ice
Th
e F
un
dam
enta
l Co
un
tin
g P
rin
cip
leU
se t
he
Fu
nd
amen
tal
Cou
nti
ng
Pri
nci
ple
to
fin
d t
he
tota
l n
um
ber
of
outc
omes
in
eac
h s
itu
atio
n.
1.ch
oosi
ng
from
8 c
ar m
odel
s,5
exte
rior
pai
nt
colo
rs,a
nd
2 in
teri
or c
olor
s80
2.se
lect
ing
a ye
ar i
n t
he
last
dec
ade
and
a m
onth
of
the
year
1
20
3.pi
ckin
g fr
om 3
th
eme
park
s an
d 1-
day,
2-da
y,3-
day,
and
5-da
y pa
sses
1
2
4.ch
oosi
ng
a m
eat
and
chee
se s
andw
ich
fr
om t
he
list
sh
own
in
th
e ta
ble
16
5.to
ssin
g a
coin
an
d ro
llin
g 2
nu
mbe
r cu
bes
72
6.se
lect
ing
coff
ee i
n r
egu
lar
or d
ecaf
,wit
h o
r w
ith
out
crea
m,a
nd
wit
h o
rw
ith
out
swee
ten
ers
8
7C
OIN
SF
ind
the
nu
mbe
r of
pos
sibl
e ou
tcom
es i
f 2
quar
ters
,4 d
imes
,an
d 1
nic
kel
are
toss
ed.
27�
128
8.SO
CIA
L SE
CU
RIT
YF
ind
the
nu
mbe
r of
pos
sibl
e 9-
digi
t so
cial
sec
uri
tyn
um
bers
if
the
digi
ts m
ay b
e re
peat
ed.
109
or
1,00
0,00
0,00
0
9.A
IRPO
RTS
Jolo
n w
ill
be s
tayi
ng
wit
h h
is g
ran
dpar
ents
for
a w
eek.
Th
ere
are
fou
r fl
igh
ts t
hat
lea
ve t
he
airp
ort
nea
r Jo
lon
's h
ome
that
con
nec
t to
an a
irpo
rt t
hat
has
tw
o di
ffer
ent
flig
hts
to
his
gra
ndp
aren
ts’ h
omet
own
.F
ind
the
nu
mbe
r of
pos
sibl
e fl
igh
ts.T
hen
fin
d th
e pr
obab
ilit
y of
tak
ing
the
earl
iest
fli
ght
from
eac
h a
irpo
rt i
f th
e fl
igh
t is
sel
ecte
d at
ran
dom
.
8;�1 8�
10.
AN
ALY
ZE T
AB
LES
Th
e ta
ble
show
s th
e ki
nds
of
hom
es o
ffer
ed b
y a
resi
den
tial
bu
ilde
r.If
th
e bu
ilde
r of
fers
a d
isco
un
t on
on
e h
ome
at r
ando
m,f
ind
the
prob
abil
ity
it w
ill
be a
4-b
edro
om
hom
e w
ith
an
ope
n p
orch
.Exp
lain
yo
ur
reas
onin
g.
Sam
ple
an
swer
:Th
e bu
ilder
off
ers
3�
4 �
2 �
24 k
ind
s o
fh
om
es.T
he
dis
cou
nte
d h
om
e h
as 1
ch
oic
e fo
r th
e n
um
ber
o
f b
edro
om
s,4
cho
ices
fo
r th
e st
yle
of
kitc
hen
,an
d 1
ch
oic
efo
r th
e ty
pe
of
po
rch
.Sin
ce 1
�4
�1
�4,
the
pro
bab
ility
is � 24 4�
��1 6� .
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
924
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-3
Nu
mb
er o
f S
tyle
of
Typ
e of
Bed
room
sK
itch
enP
orch
5-be
droo
mM
edit
erra
nea
nO
pen
4-be
droo
mC
onte
mpo
rary
Scr
een
3-be
droo
mS
outh
wes
tern
Col
onia
l
Ch
eese
Mea
tP
rovo
lon
eS
alam
iS
wis
sT
urk
eyA
mer
ican
Tu
na
Ch
edda
rH
am
6SD
AP
3.1
Prac
tice
Th
e F
un
dam
enta
l Co
un
tin
g P
rin
cip
le
Answers (Lesson 9-3)
Chapter 9 A9 Glencoe California Mathematics, Grade 6
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Less
on R
eadi
ng G
uide
Per
mu
tati
on
s
Cha
pter
927
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Lesson 9–4
pygp
9-4
Get
Rea
dy
for
the
Less
on
Com
ple
te t
he
Min
i L
ab a
t th
e to
p o
f p
age
475
in y
our
text
boo
k.W
rite
you
r an
swer
s b
elow
.
1.W
hen
you
fir
st s
tart
ed t
o m
ake
you
r li
st,h
ow m
any
choi
ces
did
you
hav
efo
r yo
ur
firs
t cl
ass?
3
2.O
nce
you
r fi
rst
clas
s w
as s
elec
ted,
how
man
y ch
oice
s di
d yo
u h
ave
for
the
seco
nd
clas
s? T
hen
,th
e th
ird
clas
s?2;
1
Rea
d t
he
Less
on
3.E
xpla
in w
hy
the
arra
nge
men
t S
cien
ce,M
ath
,Lan
guag
e A
rts
is a
perm
uta
tion
of
Mat
h,S
cien
ce,L
angu
age
Art
s.T
he
ord
er o
f th
ecl
asse
s is
dif
fere
nt.
4.In
Exa
mpl
e 1
on p
age
475,
wh
y is
th
ere
only
1 c
hoi
ce f
or t
he
thir
d cl
ass?
Sam
ple
an
swer
:S
ince
th
ere
are
on
ly t
hre
e cl
asse
s,o
nly
1ch
oic
e re
mai
ns
for
the
thir
d c
lass
.
5.In
Exa
mpl
e 2
on p
age
476,
wh
y ar
e th
ere
only
7 c
hoi
ces
for
seco
nd
plac
e?S
amp
le a
nsw
er:T
her
e ar
e o
nly
8 s
wim
mer
s,an
d o
ne
of
them
com
es in
fir
st p
lace
.Th
at p
erso
n c
ann
ot
com
e in
sec
on
dp
lace
as
wel
l.S
o,t
her
e ar
e o
nly
7 s
wim
mer
s le
ft
that
co
uld
co
me
in s
eco
nd
pla
ce.
Rem
emb
er W
hat
Yo
u L
earn
ed6.
Loo
k u
p th
e w
ord
perm
ute
in a
dic
tion
ary.
How
doe
s th
e m
ean
ing
of t
his
wor
d re
late
to
the
con
cept
s in
th
is l
esso
n,e
spec
iall
y th
e co
nce
pt o
fpe
rmu
tati
ons?
Sam
ple
an
swer
:Th
e w
ord
per
mu
te m
ean
s to
arra
ng
e in
all
po
ssib
le w
ays.
A p
erm
uta
tio
n is
th
e lis
tin
g o
fal
l of
thes
e ar
ran
gem
ents
.
6SDAP3.1
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Enri
chm
ent
Cha
pter
926
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-3
Cu
rio
us
Cu
bes
If a
six
-fac
ed c
ube
is
roll
ed a
ny
nu
mbe
r of
tim
es,t
he
theo
reti
cal
prob
abil
ity
ofth
e cu
be l
andi
ng
on a
ny
give
n f
ace
is �1 6�.
Eac
h c
ub
e b
elow
has
six
fac
es a
nd
has
bee
n r
olle
d 1
00 t
imes
.Th
eou
tcom
es h
ave
bee
n t
alli
ed a
nd
rec
ord
ed i
n a
fre
qu
ency
tab
le.B
ased
on t
he
dat
a in
eac
h f
req
uen
cy t
able
,wh
at c
an y
ou s
ay a
re p
rob
ably
on t
he
un
seen
fac
es o
f ea
ch c
ub
e?
1.
Th
e fa
ces
are
nu
mb
ered
2,
3,an
d 6
.
2.T
her
e ar
e tw
o y
ello
wfa
ces
and
on
e re
d f
ace.
3.
Th
e fa
ces
are
bla
nk.
4.
Th
e fa
ces
are
nu
mb
ered
1,
4,an
d 5
.
5.
On
e fa
ce is
nu
mb
ered
2
and
tw
o f
aces
are
b
lan
k.1
4
5
14
5
Blue
Red
Red
Yello
wBlue
Red
14
5O
utc
ome
Tal
ly1
152
143
184
165
196
18
Ou
tcom
eT
ally
blu
e17
red
30
yell
ow53
Ou
tcom
eT
ally
red
30
blu
e16
blan
k54
Ou
tcom
eT
ally
134
432
534
Ou
tcom
eT
ally
114
513
418
216
blan
k39
6SD
AP
3.1
Answers (Lessons 9-3 and 9-4)
Chapter 9 A10 Glencoe California Mathematics, Grade 6
An
swer
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Skill
s Pr
actic
eP
erm
uta
tio
ns
Cha
pter
929
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Lesson 9–4
pygp
9-4
Fin
d t
he
valu
e of
eac
h e
xpre
ssio
n.
1.2
· 12
2.4
· 3 ·
2 · 1
24
3.3
· 2 ·
1 · 5
· 4
· 3 ·
2 · 1
720
4.9
· 8 ·
7 · 6
· 5
· 4 ·
3 · 2
· 1
362,
880
5.2
· 1 ·
8 · 7
· 6
· 5 ·
4 · 3
· 2
· 180
,640
6.3
· 2 ·
1 · 2
· 1
12
7.11
· 10
· 9
990
8.10
· 9
· 8 ·
7 · 6
· 5
· 4 ·
3 · 2
· 1
3,62
8,80
0
9.5
· 4 ·
3 · 2
· 1
· 2 ·
124
010
.5
· 4 ·
3 · 2
120
11.
8 · 7
· 6
· 5 ·
4 · 3
· 2
· 140
,320
12.
6 · 5
· 4
· 3 ·
2 · 1
720
13.
How
man
y w
ays
can
you
arr
ange
th
e le
tter
s in
th
e w
ord
PR
IME
?12
0
14.
How
man
y w
ays
can
you
arr
ange
8 d
iffe
ren
t cr
ates
on
a s
hel
f if
th
ey a
repl
aced
fro
m l
eft
to r
igh
t?40
,320
6SDAP3.1
Exer
cise
s
Exam
ple
2
Exam
ple
3
Exam
ple
1
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Per
mu
tati
on
s
Cha
pter
928
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-4
Fin
d t
he
valu
e of
5 �
4 �
3 �
2 �
1.
5�
4�
3�
2�
1�
120
Sim
plify
.
Fin
d t
he
valu
e of
4 �
3�
2 �
1 �
2 �
1.
4�
3�
2�
1�
2�
1�
48S
impl
ify.
BO
OK
SH
ow m
any
way
s ca
n 4
dif
fere
nt
boo
ks
be
arra
nge
d o
n a
boo
ksh
elf?
Th
is i
s a
perm
uta
tion
.Su
ppos
e th
e bo
oks
are
plac
ed o
n t
he
shel
f fr
om l
eft
to r
igh
t.T
here
are
4ch
oice
s fo
r th
e fir
st b
ook.
The
re a
re 3
choi
ces
that
rem
ain
for
the
seco
nd b
ook.
The
re a
re 2
choi
ces
that
rem
ain
for
the
third
boo
k.T
here
is 1
choi
ce t
hat
rem
ains
for
the
four
th b
ook.
4�
3�
2�
1�
24
Sim
plify
.
So,
ther
e ar
e 24
way
s to
arr
ange
4 d
iffe
ren
t bo
oks
on a
boo
ksh
elf.
Fin
d t
he
valu
e of
eac
h e
xpre
ssio
n.
1.3
· 2 ·
16
2.7
· 6 ·
5 · 4
· 3
· 2 ·
15,
040
3.6
· 5 ·
4 · 3
· 2
· 1 ·
3 · 2
· 1
4,32
04.
9 · 8
· 7
504
5.H
ow m
any
way
s ca
n y
ou a
rran
ge t
he
lett
ers
in t
he
wor
d G
RO
UP
?12
0
6.H
ow m
any
diff
eren
t 4-
digi
t n
um
bers
can
be
crea
ted
if n
o di
git
can
be
repe
ated
? R
emem
ber,
a n
um
ber
can
not
beg
in w
ith
0.
4,53
6
A p
erm
uta
tio
nis
an
arra
ngem
ent,
or li
stin
g, o
f ob
ject
s in
whi
ch o
rder
is im
port
ant.
You
can
use
the
Fun
dam
enta
l Cou
ntin
g P
rinci
ple
to f
ind
the
num
ber
of p
ossi
ble
arra
ngem
ents
.
6SDAP3.1
Answers (Lesson 9-4)
Chapter 9 A11 Glencoe California Mathematics, Grade 6
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Wor
d Pr
oble
m P
ract
ice
Per
mu
tati
on
s
Cha
pter
931
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Lesson 9–4
pygp
9-4
1.A
REA
CO
DES
How
man
y di
ffer
ent
3-di
git
area
cod
es c
an b
e cr
eate
d if
no
digi
t ca
n b
e re
peat
ed?
720
2.C
AR
DS
Jaso
n i
s de
alt
five
pla
yin
gca
rds.
In h
ow m
any
diff
eren
t or
ders
cou
ld J
ason
hav
e be
en d
ealt
th
e sa
me
han
d?12
0
3.PA
SSW
OR
DS
How
man
y di
ffer
ent
3-le
tter
pas
swor
ds a
re p
ossi
ble
if n
ole
tter
may
be
repe
ated
?15
,600
4.R
AC
ING
All
22
stu
den
ts i
n A
my’
s cl
ass
are
goin
g to
ru
n t
he
100-
met
er d
ash
.In
how
man
y w
ays
can
th
e st
ude
nts
fin
ish
in f
irst
,sec
ond,
and
thir
d pl
ace?
9,24
0
5.LE
TTER
SH
ow m
any
way
s ca
n y
ouar
ran
ge t
he
lett
ers
in t
he
wor
dH
IST
OR
Y?
5,04
0
6.PA
RK
ING
Th
e pa
rkin
g lo
t fo
r a
com
pan
yh
as t
hre
e pa
rkin
g sp
aces
for
com
pact
cars
.Th
e co
mpa
ny
has
8 e
mpl
oyee
sw
ith
com
pact
car
s.H
ow m
any
way
s ca
nth
e co
mpa
ct p
arki
ng
spac
es b
e fi
lled
?33
6
7.SE
RIA
L N
UM
BER
SH
ow m
any
diff
eren
t 6-
digi
t se
rial
nu
mbe
rs a
re a
vail
able
if
no
digi
t ca
n b
e re
peat
ed?
151,
200
8.W
INN
ERS
Th
ere
are
156
way
s fo
r 2
cars
to w
in f
irst
an
d se
con
d pl
ace
in a
rac
e.H
ow m
any
cars
are
in
th
e ra
ce?
13
6SDAP3.1
Sol
ve e
ach
pro
ble
m.
1.N
UM
BER
SH
ow m
any
diff
eren
t 2-
digi
t n
um
bers
can
be
form
ed f
rom
th
edi
gits
4,6
,an
d 8?
Ass
um
e n
o n
um
ber
can
be
use
d m
ore
than
on
ce.
6
2.LE
TTER
SH
ow m
any
perm
uta
tion
s ar
e po
ssib
le o
f th
e le
tter
s in
th
e w
ord
NU
MB
ER
S?
7! o
r 5,
040
3.PA
SSEN
GER
ST
her
e ar
e 5
pass
enge
rs i
n a
car
.In
how
man
y w
ays
can
th
epa
ssen
gers
sit
in
th
e 5
pass
enge
r se
ats
of t
he
car?
5! o
r 12
0
4.PA
INTI
NG
SM
r.B
ern
stei
n o
wn
s 14
pai
nti
ngs
,bu
t h
as o
nly
en
ough
wal
lsp
ace
in h
is h
ome
to d
ispl
ay t
hre
e of
th
em a
t an
y on
e ti
me:
one
in t
he
hal
lway
,on
e in
th
e de
n,a
nd
one
in t
he
parl
or.H
ow m
any
way
s ca
n M
r.B
ern
stei
n d
ispl
ay t
hre
e pa
inti
ngs
in
his
hom
e?2,
184
5.D
OG
SH
OW
Mat
eo i
s on
e of
th
e si
x do
g ow
ner
s in
th
e te
rrie
r ca
tego
ry.I
fth
e ow
ner
s ar
e se
lect
ed i
n a
ran
dom
ord
er t
o sh
ow t
hei
r do
gs,h
ow m
any
way
s ca
n t
he
own
ers
show
th
eir
dogs
?6!
or
720
6.TI
ME
Mic
hel
,Jon
ath
an,a
nd
two
of t
hei
r fr
ien
ds e
ach
rid
e th
eir
bike
s to
sch
ool.
If t
hey
hav
e an
equ
ally
-lik
ely
chan
ce o
f ar
rivi
ng
firs
t,w
hat
is
the
prob
abil
ity
that
Jon
ath
an w
ill
arri
ve f
irst
an
d M
ich
el w
ill
arri
vese
con
d?� 11 2�
7.B
IRTH
DA
YG
len
rec
eive
d 6
birt
hda
y ca
rds.
If h
e is
equ
ally
lik
ely
to r
ead
the
card
s in
an
y or
der,
wh
at i
s th
e pr
obab
ilit
y h
e re
ads
the
card
fro
m h
ispa
ren
ts a
nd
the
card
fro
m h
is s
iste
r be
fore
th
e ot
her
car
ds?
CO
DES
For
Exe
rcis
es 8
–10,
use
th
e fo
llow
ing
info
rmat
ion
.A b
ank
giv
esea
ch n
ew c
ust
omer
a 4
-dig
it c
ode
nu
mb
er w
hic
h a
llow
s th
e n
ewcu
stom
er t
o cr
eate
th
eir
own
pas
swor
d.T
he
cod
e n
um
ber
is
assi
gned
ran
dom
ly f
rom
th
e d
igit
s 1,
3,5,
and
7,a
nd
no
dig
it i
s re
pea
ted
.
8.W
hat
is
the
prob
abil
ity
that
th
e co
de n
um
ber
for
a n
ew c
ust
omer
wil
lbe
gin
or
end
wit
h a
7?
�1 2�
9.W
hat
is
the
prob
abil
ity
that
th
e co
de n
um
ber
wil
l n
otco
nta
in a
5?
0
10.
Wh
at i
s th
e pr
obab
ilit
y th
at t
he
code
nu
mbe
r w
ill
star
t w
ith
371
?� 21 4�
1 � 30
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Prac
tice
Per
mu
tati
on
s
Cha
pter
930
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-4
6SD
AP
3.1
Answers (Lesson 9-4)
Chapter 9 A12 Glencoe California Mathematics, Grade 6
An
swer
s
Exer
cise
s
Exam
ple
1
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
TI-8
3/84
Plu
s A
ctiv
ityP
erm
uta
tio
ns
Cha
pter
933
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Lesson 9–4
pygp
9-4
You
can
use
a g
raph
ing
calc
ulat
or t
o he
lp y
ou f
ind
the
num
ber
of p
erm
utat
ions
.
25 p
eopl
e ar
e au
diti
onin
g fo
r 5
diff
eren
t pa
rts
in a
pl
ay.I
n ho
w m
any
way
s ca
n th
e 5
part
s be
ass
igne
d?
To c
alcu
late
a p
erm
utat
ion,
fin
d th
e to
tal n
umbe
r of
obje
cts
(n)
and
the
num
ber
take
n at
one
tim
e (r
). I
n th
ispr
oble
m, n
�25
. Bec
ause
5 s
tude
nts
are
need
ed, r
�5.
Ent
er:2
5 2
5 6,
375,
600
The
par
ts c
an b
e as
sign
ed in
6,3
75,6
00 d
iffe
rent
way
s.
Fin
d t
he
valu
e of
eac
h p
erm
uta
tion
for
th
e gi
ven
val
ues
of
nan
d r
.
1.n
�5,
r�
220
2.n
�8,
r�
333
63.
n�
9, r
�6
60,4
80
4.n
�6,
r�
230
5.n
�10
, r�
615
1,20
06.
n�
12, r
�4
11,8
80
7.n
�20
, r�
238
08.
n�
15, r
�7
32,4
32,4
009.
n�
18, r
�3
4,89
6
Sol
ve.
10.
Em
ploy
ees
of S
pies
, Inc
., ar
e gi
ven
3-di
git c
ode
num
bers
mad
e up
of
the
digi
ts 1
, 3, 5
, 7, a
nd 9
. How
man
y di
ffer
ent 3
-dig
it c
ode
num
bers
can
be c
reat
ed?
60
11.
How
man
y di
ffer
ent 4
-let
ter
arra
ngem
ents
are
ther
e in
the
lett
ers
A, S
,N
, D, T
, R, a
nd Y
?84
0
12.
Twen
ty s
tude
nts
have
ent
ered
an
art c
onte
st. F
ive
stud
ents
wil
l eac
hre
ceiv
e di
ffer
ent a
war
ds. H
ow m
any
diff
eren
t gro
ups
of 5
stu
dent
sco
uld
be s
elec
ted
to r
ecei
ve a
war
ds?
1,86
0,48
0
EN
TER
MA
TH
Cyc
lic P
erm
uta
tio
ns
1.G
eorg
e,A
lan
,an
d W
illi
am a
re i
n t
he
sam
e m
ath
cla
ss.G
eorg
e h
as f
ive
diff
eren
t sh
irts
an
d w
ears
a d
iffe
ren
t on
e ea
ch d
ay.I
n h
ow m
any
way
sca
n G
eorg
e w
ear
his
fiv
e sh
irts
in
fiv
e da
ys?
5 �
4 �
3 �
2 �
1 �
120
way
s2.
Ala
n h
as t
hre
e di
ffer
ent
shir
ts a
nd
Wil
liam
has
fou
r.W
hic
h o
f th
e th
ree
stu
den
ts,G
eorg
e,A
lan
,or
Wil
liam
,goe
s th
e gr
eate
st n
um
ber
of d
ays
befo
re h
e h
as t
o w
ear
a sh
irt
for
the
seco
nd
tim
e? E
xpla
in.
Geo
rge.
Ala
n c
an w
ear
his
sh
irts
in 3
�2
�1
�6
dif
fere
nt
way
s,an
d W
illia
m c
an w
ear
his
sh
irts
in 4
�3
�2
�1
�24
dif
fere
nt
way
s.G
eorg
e,A
lan
,an
d W
illi
am a
lway
s w
ear
thei
r sh
irts
in
th
e sa
me
orde
r.S
upp
ose
that
Geo
rge’
s 5
shir
ts a
re r
ed,t
an,g
reen
,bla
ck,a
nd
wh
ite.
He
wea
rs h
is s
hir
ts f
ollo
win
g th
is p
atte
rn:
B W
R T
G B
W R
T …
No
mat
ter
wh
ere
Geo
rge
is i
n t
he
patt
ern
,his
fri
ends
can
alw
ays
figu
re o
ut
wh
ich
sh
irt
Geo
rge
wil
l w
ear
nex
t.S
ince
th
ese
perm
uta
tion
s ar
e th
e sa
me
wh
en t
hey
mak
e u
p pa
rt o
f a
cycl
e,th
ey a
re c
alle
d cy
clic
per
mu
tati
ons.
3.A
lan
has
sh
irts
th
at a
re w
hit
e,bl
ack,
and
purp
le.M
ake
an o
rgan
ized
lis
tof
all
th
e di
ffer
ent
perm
uta
tion
s.
WB
P;
BW
P;
PW
B a
nd
WP
B;
BP
W;
PB
W4.
How
man
y di
ffer
ent
way
s ar
e th
ere
for
Ala
n t
o w
ear
his
sh
irts
so
that
his
frie
nds
rec
ogn
ize
diff
eren
t pa
tter
ns?
Exp
lain
.
2 w
ays;
WB
P,B
PW
an
d P
WB
are
cyc
lic p
erm
uta
tio
ns,
and
WP
B,B
WP
an
d P
BW
are
cyc
lic p
erm
uta
tio
ns.
5.W
illi
am h
as a
thle
tic
shir
ts t
hat
are
lab
eled
1,2
,3,a
nd
4.M
ake
anor
gan
ized
lis
t of
all
th
e di
ffer
ent
perm
uta
tion
s.12
34;
2134
;31
24;
4123
1342
;23
41;
3241
;42
3112
43;
2143
;31
42;
4132
1423
;24
13;
3412
;43
1213
24;
2314
;32
14;
4213
1432
;24
31;
3421
;43
21
6.H
ow m
any
diff
eren
t w
ays
are
ther
e fo
r W
illi
am t
o w
ear
his
sh
irts
so
that
his
frie
nds
rec
ogn
ize
diff
eren
t pa
tter
ns?
Exp
lain
.6
way
s;12
34,1
243,
1324
,13
42,1
423
and
143
2 ar
e u
niq
ue
cycl
es.A
ll o
ther
per
mu
tati
on
s ca
nb
e w
ritt
en a
s o
ne
of
thes
e,bu
t in
a d
iffe
ren
t o
rder
.7.
CH
ALL
ENG
EF
or a
ny
give
n n
um
ber
of s
hir
ts,h
ow c
an y
ou d
eter
min
e th
en
um
ber
of w
ays
a pe
rson
cou
ld w
ear
the
shir
ts t
o pr
odu
ce u
niq
ue
patt
ern
s?Ta
ke t
he
fact
ori
al o
f o
ne
less
th
an t
he
nu
mb
er o
fsh
irts
,th
at is
(n
�1)
!.
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Enri
chm
ent
Cha
pter
932
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-4
6SD
AP
3.1
Answers (Lesson 9-4)
Chapter 9 A13 Glencoe California Mathematics, Grade 6
Exer
cise
s
Jil
l w
as a
sked
by
her
tea
cher
to
choo
se 3
top
ics
from
th
e 8
top
ics
give
n t
o h
er.H
ow m
any
dif
fere
nt
thre
e-to
pic
gr
oup
s co
uld
sh
e ch
oose
?
Th
ere
are
8 · 7
· 6
perm
uta
tion
s of
th
ree-
topi
c gr
oups
ch
osen
fro
m e
igh
t.T
her
e ar
e 3
· 2 ·
1w
ays
to a
rran
ge t
he
grou
ps.
�8�7
�6
� �
�33 66 � �
56
So,
ther
e ar
e 56
dif
fere
nt
thre
e-to
pic
grou
ps.
Tel
l w
het
her
eac
h s
itu
atio
n r
epre
sen
ts a
per
mu
tati
onor
com
bin
ati
on.
Th
en s
olve
th
e p
rob
lem
.
On
a q
uiz
,you
are
all
owed
to
answ
er a
ny
4 ou
t of
th
e 6
qu
esti
ons.
How
man
y w
ays
can
you
ch
oose
th
e q
ues
tion
s?
Th
is i
s a
com
bin
atio
n b
ecau
se t
he
orde
r of
th
e 4
ques
tion
s is
not
im
port
ant.
So,
ther
e ar
e 6
· 5 ·
4 · 3
per
mu
tati
ons
of f
our
ques
tion
s ch
osen
fro
m s
ix.T
her
e ar
e 4
· 3 ·
2 · 1
ord
ers
inw
hic
h t
hes
e qu
esti
ons
can
be
chos
en.
�6�
5 4� !4�
3�
�
�3 26 40 � �
15
So,
ther
e ar
e 15
way
s to
ch
oose
th
e qu
esti
ons.
Fiv
e d
iffe
ren
t ca
rs e
nte
r a
par
kin
g lo
t w
ith
on
ly 3
em
pty
sp
aces
.H
ow m
any
way
s ca
n t
hes
e sp
aces
be
fill
ed?
Th
is i
s a
perm
uta
tion
bec
ause
eac
h a
rran
gem
ent
of t
he
sam
e 3
cars
cou
nts
as
a di
stin
ctar
rran
gem
ent.
So,
ther
e ar
e 5
· 4 ·
3 or
60
way
s th
e sp
aces
can
be
fill
ed.
Tel
l w
het
her
eac
h s
itu
atio
n r
epre
sen
ts a
per
mu
tati
onor
com
bin
ati
on.
Th
en s
olve
th
e p
rob
lem
.
1.H
ow m
any
way
s ca
n 4
peo
ple
be c
hos
en f
rom
a g
rou
p of
11?
com
bin
atio
n;
330
2.H
ow m
any
way
s ca
n 3
peo
ple
sit
in 4
ch
airs
?p
erm
uta
tio
n;
24
3.H
ow m
any
way
s ca
n 2
gol
dfis
h b
e ch
osen
fro
m a
tan
k co
nta
inin
g 15
gol
dfis
h?
com
bin
atio
n;
105
Exam
ple
2
Exam
ple
3
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Co
mb
inat
ion
s
Cha
pter
935
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Lesson 9–5
pygp
9-5
An
arra
ngem
ent,
or li
stin
g, o
f ob
ject
s in
whi
ch o
rder
is n
otim
port
ant
is c
alle
d a
com
bin
atio
n.Y
ou c
anfin
d th
e nu
mbe
r of
com
bina
tions
of
obje
cts
by d
ivid
ing
the
num
ber
of p
erm
utat
ions
of
the
entir
e se
t by
the
num
ber
of w
ays
each
sm
alle
r se
t ca
n be
arr
ange
d.
Exam
ple
1
6SDAP3.1
3�
2�
1
4�
3�
2 �
1
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Less
on R
eadi
ng G
uide
Co
mb
inat
ion
s
Cha
pter
934
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-5
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n a
t th
e to
p o
f p
age
480
in y
our
text
boo
k.W
rite
you
r an
swer
s b
elow
.
1.U
se t
he
firs
t le
tter
of
each
nam
e to
lis
t al
l of
th
e pe
rmu
tati
ons
of
co-c
apta
ins.
How
man
y ar
e th
ere?
JB,J
O,J
D,B
J,B
O,B
D,O
J,O
B,
OD
,DJ,
DB
,DO
;12
2.C
ross
ou
t an
y ar
ran
gem
ent
that
con
tain
s th
e sa
me
lett
ers
as a
not
her
on
ein
th
e li
st.H
ow m
any
are
ther
e n
ow?
6
3.E
xpla
in t
he
diff
eren
ce b
etw
een
th
e tw
o li
sts
abov
e.T
he
list
inE
xerc
ise
1 is
a p
erm
uta
tio
n w
her
e o
rder
is im
po
rtan
t.T
he
list
in E
xerc
ise
2 d
oes
no
t ta
ke o
rder
into
acc
ou
nt.
Rea
d t
he
Less
on
4.H
ow c
an y
ou f
ind
the
nu
mbe
r of
com
bin
atio
ns
of o
bjec
ts i
n a
set
?S
amp
le a
nsw
er:
Div
ide
the
nu
mb
er o
f p
erm
uta
tio
ns
of
the
enti
re s
et b
y th
e n
um
ber
of
way
s ea
ch s
mal
ler
set
can
be
arra
ng
ed.
5.W
hy
mig
ht
it b
e ea
sier
to
calc
ula
te t
he
nu
mbe
r of
com
bin
atio
ns
of a
set
of
obje
cts
usi
ng
a pe
rmu
tati
on r
ath
er t
han
mak
ing
a li
st?
Sam
ple
answ
er:
A li
st c
ou
ld b
e q
uit
e le
ng
thy,
dep
end
ing
on
th
en
um
ber
of
ob
ject
s in
th
e se
t an
d t
he
nu
mb
er o
f th
em b
ein
gch
ose
n.
For
Exe
rcis
es 6
an
d 7
,ref
er t
o E
xam
ple
2 o
n p
age
525
in y
our
text
boo
k.
6.In
th
e di
agra
m,h
ow m
any
poin
ts a
re t
her
e? H
ow m
any
lin
e se
gmen
tsco
nn
ect
to a
ny
one
poin
t?8;
7
7.H
ow d
oes
you
r an
swer
to
Exe
rcis
e 6
abov
e co
rres
pon
d to
Exa
mpl
e 2
inyo
ur
book
?T
her
e ar
e 8
· 7 w
ays
to c
ho
ose
2 p
eop
le.
Rem
emb
er W
hat
Yo
u L
earn
ed8.
Wor
k w
ith
a p
artn
er.T
ake
turn
s th
inki
ng
of s
itu
atio
ns
in w
hic
h a
sele
ctio
n f
rom
a g
rou
p m
ust
be
mad
e,w
her
e or
der
is o
r is
not
im
port
ant.
Tel
l ea
ch o
ther
wh
ich
sit
uat
ion
s ar
e pe
rmu
tati
ons
and
wh
ich
are
com
bin
atio
ns.
Sol
ve e
ach
pro
blem
an
d sh
ow y
our
wor
k.S
ee s
tud
ents
’wo
rk.
6SD
AP
3.1
Answers (Lesson 9-5)
Chapter 9 A14 Glencoe California Mathematics, Grade 6
An
swer
s
Sol
ve e
ach
pro
ble
m.
1.B
ASK
ETB
ALL
In h
ow m
any
way
s ca
n a
coa
ch s
elec
t 5
play
ers
from
a t
eam
of 1
0 pl
ayer
s? 25
2
2.B
OO
KS
In h
ow m
any
way
s ca
n 3
boo
ks b
e se
lect
ed f
rom
a s
hel
f of
25
book
s?
2,30
0
3.C
AFE
TER
IAIn
how
man
y w
ays
can
you
ch
oose
2 s
ide
dish
es f
rom
15
item
s?10
5
4.C
HO
RES
Of
8 h
ouse
hol
d ch
ores
,in
how
man
y w
ays
can
you
do
thre
e-fo
urt
hs
of t
hem
? 2
8
5.EL
DER
LYL
atan
ya v
olu
nte
ers
to b
ake
and
deli
ver
past
ries
to
elde
rly
peop
lein
her
nei
ghbo
rhoo
d.In
how
man
y di
ffer
ent
way
s ca
n L
atan
ya d
eliv
er t
o2
of t
he
6 el
derl
y pe
ople
in
her
nei
ghbo
rhoo
d? 15
6.D
ELI
A d
eli
mak
es p
otat
o,m
acar
oni,
thre
e be
an,C
aesa
r,7-
laye
r,an
dG
reek
sal
ads.
Th
e de
li r
ando
mly
mak
es o
nly
fou
r sa
lads
eac
h d
ay.W
hat
is
the
prob
abil
ity
that
th
e fo
ur
sala
ds m
ade
one
day
are
7-la
yer,
mac
aron
i,G
reek
,an
d po
tato
?� 11 5�
7.A
UTO
GR
APH
SA
spo
rts
mem
orab
ilia
en
thu
sias
t co
llec
ted
auto
grap
hed
bas
ebal
ls f
rom
th
e pl
ayer
s in
th
e ta
ble.
Th
e en
thu
sias
t is
giv
ing
one
auto
grap
hed
ba
seba
ll t
o ea
ch o
f h
is t
hre
e gr
andc
hil
dren
.If
the
base
ball
s ar
e se
lect
ed a
t ra
ndo
m,w
hat
is
the
prob
abil
ity
that
th
e H
ank
Aar
on,A
lex
Rod
riqu
ez,
and
Mic
key
Man
tle
auto
grap
hed
bas
ebal
ls a
re g
iven
to
his
gra
ndc
hil
dren
?� 11 0�
For
Exe
rcis
es 8
–10,
tell
wh
eth
er e
ach
pro
ble
m r
epre
sen
ts a
per
mu
tati
onor
a c
ombi
na
tion
.Th
en s
olve
th
e p
rob
lem
.
8.LO
CK
SIn
how
man
y w
ays
can
th
ree
diff
eren
t n
um
bers
be
sele
cted
fro
m10
nu
mbe
rs t
o op
en a
key
pad
lock
? p
erm
uta
tio
n;
720
9.M
OV
IES
How
man
y w
ays
can
10
DV
Ds
be p
lace
d on
a s
hel
f?p
erm
uta
tio
n;
10!
or
3,62
8,80
0
10.
TRA
NSP
OR
TATI
ON
Eig
ht
peop
le n
eed
tran
spor
tati
on t
o th
e co
nce
rt.H
owm
any
diff
eren
t gr
oups
of
6 pe
ople
can
rid
e w
ith
Mrs
.Joh
nso
n?
com
bin
atio
n;
28
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Prac
tice
Co
mb
inat
ion
s
Cha
pter
937
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Lesson 9–5
pygp
9-5
Pla
yer
Cal
Rip
kin
Han
k A
aron
Bar
ry B
onds
Ale
x R
odri
quez
Mic
key
Man
tle
6SD
AP
3.1
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Skill
s Pr
actic
eC
om
bin
atio
ns
Cha
pter
936
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-5
Tel
l w
het
her
eac
h s
itu
atio
n r
epre
sen
ts a
per
mu
tati
onor
com
bin
ati
on.
Th
en s
olve
th
e p
rob
lem
.
1.Yo
u a
re a
llow
ed t
o om
it t
wo
out
of 1
2 qu
esti
ons
on a
qu
iz.H
ow m
any
way
s ca
n y
ou s
elec
t th
e qu
esti
ons
to o
mit
?co
mb
inat
ion
;66
2.S
ix s
tude
nts
are
to
be c
hos
en f
rom
a c
lass
of
18 t
o re
pres
ent
the
clas
s at
am
ath
con
test
.How
man
y w
ays
can
th
e si
x st
ude
nts
be
chos
en?
com
bin
atio
n;
18,5
64
3.H
ow m
any
diff
eren
t 5-
digi
t zi
p co
des
are
poss
ible
if
no
digi
ts a
rere
peat
ed?
per
mu
tati
on
;30
,240
4.In
a r
ace
wit
h s
ix r
un
ner
s,h
ow m
any
way
s ca
n t
he
run
ner
s fi
nis
h f
irst
,se
con
d,or
th
ird?
per
mu
tati
on
;12
0
5.H
ow m
any
way
s ca
n t
wo
nam
es b
e ch
osen
fro
m 7
6 in
a r
affl
e if
on
ly o
ne
entr
y pe
r pe
rson
is
allo
wed
?co
mb
inat
ion
;2,
850
6.H
ow m
any
way
s ca
n s
ix s
tude
nts
be
arra
nge
d in
a l
un
ch l
ine?
per
mu
tati
on
;72
0
7.A
fam
ily
has
a b
ike
rack
th
at f
its
seve
n b
ikes
bu
t th
ey o
nly
hav
e fi
vebi
kes.
How
man
y w
ays
can
th
e bi
kes
fit
in t
he
bike
rac
k?p
erm
uta
tio
n;
2,52
0
8.H
ow m
any
way
s ca
n y
ou s
elec
t th
ree
sher
iff
depu
ties
fro
m e
igh
tca
ndi
date
s?co
mb
inat
ion
;56
9.H
ow m
any
way
s ca
n f
our
fin
alis
ts b
e se
lect
ed f
rom
50
con
test
ants
?co
mb
inat
ion
;23
0,30
0
10.
How
man
y 4-
digi
t pi
n n
um
bers
are
ava
ilab
le i
f n
o n
um
ber
is r
epea
ted?
per
mu
tati
on
;5,
040
11.
How
man
y h
ands
hak
es c
an o
ccu
r be
twee
n f
ive
peop
le i
f ev
eryo
ne
shak
esh
ands
?co
mb
inat
ion
;10
6SD
AP
3.1
Answers (Lesson 9-5)
Chapter 9 A15 Glencoe California Mathematics, Grade 6
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Enri
chm
ent
Cha
pter
939
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Lesson 9–5
pygp
9-5
Fro
m Im
po
ssib
le t
o C
erta
in E
ven
tsA
pro
babi
lity
is
ofte
n e
xpre
ssed
as
a fr
acti
on.A
s yo
u k
now
,an
eve
nt
that
is
impo
ssib
le i
s gi
ven
a p
roba
bili
ty o
f 0
and
an e
ven
t th
at i
s ce
rtai
n i
s gi
ven
apr
obab
ilit
y of
1.E
ven
ts t
hat
are
nei
ther
im
poss
ible
nor
cer
tain
are
giv
en a
prob
abil
ity
som
ewh
ere
betw
een
0 a
nd
1.T
he
prob
abil
ity
lin
e be
low
sh
ows
rela
tive
pro
babi
liti
es.
Det
erm
ine
the
pro
bab
ilit
y of
an
eve
nt
by
con
sid
erin
g it
s p
lace
on
th
ed
iagr
am a
bov
e.A
nsw
ers
will
var
y.A
ccep
t lo
gic
al r
esp
on
ses.
1.M
edic
al r
esea
rch
wil
l fi
nd
a cu
re f
or a
ll d
isea
ses.
2.T
her
e w
ill
be a
per
son
al c
ompu
ter
in e
ach
hom
e by
th
e ye
ar 2
010.
3.O
ne
day,
peop
le w
ill
live
in
spa
ce o
r u
nde
r th
e se
a.
4.W
ildl
ife
wil
l di
sapp
ear
as E
arth
’s h
um
an p
opu
lati
on i
ncr
ease
s.
5.T
her
e w
ill
be a
fif
ty-f
irst
sta
te i
n t
he
Un
ited
Sta
tes.
6.T
he
sun
wil
l ri
se t
omor
row
mor
nin
g.
7.M
ost
elec
tric
ity
wil
l be
gen
erat
ed b
y n
ucl
ear
pow
er b
y th
e ye
ar 2
010.
8.T
he
fuel
eff
icie
ncy
of
auto
mob
iles
wil
l in
crea
se a
s th
e su
pply
of
gaso
lin
ede
crea
ses.
9.A
stro
nau
ts w
ill
lan
d on
Mar
s.
10.
Th
e pe
rcen
t of
hig
h s
choo
l st
ude
nts
wh
o gr
adu
ate
and
ente
r co
lleg
e w
ill
incr
ease
.
11.
Glo
bal
war
min
g pr
oble
ms
wil
l be
sol
ved.
12.
All
peo
ple
in t
he
Un
ited
Sta
tes
wil
l ex
erci
se r
egu
larl
y w
ith
in t
he
nea
rfu
ture
.
equa
lly li
kely
pret
tylik
ely
1
certa
inno
t so
likel
y
1 41 2
3 40
impo
ssib
le
6SD
AP
3.1
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Wor
d Pr
oble
m P
ract
ice
Co
mb
inat
ion
s
Cha
pter
938
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-5
1.SN
AC
KS
A v
endi
ng
mac
hin
e ca
n d
ispl
aysi
x sn
acks
.If
ther
e ar
e ei
ght
diff
eren
tki
nds
of
snac
ks a
vail
able
,how
man
ydi
ffer
ent
grou
ps o
f si
x di
ffer
ent
snac
ksca
n b
e di
spla
yed?
28
2.M
USI
CE
ach
mon
th,J
ose
purc
has
es t
wo
CD
s fr
om a
sel
ecti
on o
f 20
bes
tsel
lin
gC
Ds.
How
man
y di
ffer
ent
pair
s of
CD
sca
n J
ose
choo
se i
f h
e ch
oose
s tw
odi
ffer
ent
CD
s?19
0
3.TE
STS
On
a m
ath
tes
t,yo
u c
an c
hoo
sean
y 20
ou
t of
23
ques
tion
s.H
ow m
any
diff
eren
t gr
oups
of
20 q
ues
tion
s ca
nyo
u c
hoo
se?
1,77
1
4.R
ESTA
UR
AN
TST
he
din
ner
spe
cial
at
alo
cal
pizz
a pa
rlor
giv
es y
ou t
he
choi
ceof
tw
o to
ppin
gs f
rom
a s
elec
tion
of
six
topp
ings
.How
man
y di
ffer
ent
choi
ces
are
poss
ible
if
two
diff
eren
t to
ppin
gsar
e ch
osen
?15
5.TE
STIN
GIn
a s
cien
ce f
air
expe
rim
ent,
two
un
its
are
sele
cted
for
tes
tin
g fr
omev
ery
500
un
its
prod
uce
d.H
ow m
any
way
s ca
n t
hes
e tw
o u
nit
s be
sel
ecte
d?12
4,75
0
6.M
EETI
NG
SL
inda
’s t
each
er d
ivid
ed t
he
clas
s in
to g
rou
ps o
f fi
ve a
nd
requ
ired
each
mem
ber
of a
gro
up
to m
eet
wit
hev
ery
oth
er m
embe
r of
th
at g
rou
p.H
owm
any
mee
tin
gs w
ill
each
gro
up
hav
e?10
7.B
ASE
BA
LLA
bas
ebal
l co
ach
has
13
play
ers
to f
ill
nin
e po
siti
ons.
How
man
ydi
ffer
ent
team
s co
uld
he
put
toge
ther
?71
5
8.G
EOM
ETRY
Ten
poi
nts
are
mar
ked
on a
circ
le.H
ow m
any
diff
eren
t tr
ian
gles
can
be
draw
n b
etw
een
an
y th
ree
poin
ts?
120
6SD
AP
3.1
Answers (Lesson 9-5)
Chapter 9 A16 Glencoe California Mathematics, Grade 6
An
swer
s
Exer
cise
s
Exam
ple
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
941
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Lesson 9–6
pygp
9-6
CLO
THIN
GR
icar
do
has
tw
o sh
irts
an
d t
hre
e p
airs
of
pan
ts t
o ch
ose
from
for
his
ou
tfit
to
wea
r on
th
e fi
rst
day
of
sch
ool.
How
man
yd
iffe
ren
t ou
tfit
s ca
n h
e m
ake
by
wea
rin
g on
e sh
irt
and
on
e p
air
ofp
ants
?
By
actin
g ou
t a
prob
lem
, yo
u ar
e ab
le t
o se
e al
l pos
sibl
e so
lutio
ns t
o th
e pr
oble
m b
eing
pos
ed.
Exp
lore
We
know
th
at h
e h
as t
wo
shir
ts a
nd
thre
e pa
irs
of p
ants
to
choo
se f
rom
.We
can
use
a c
oin
for
th
e sh
irts
an
d an
equ
ally
div
ided
spi
nn
er l
abel
ed f
or t
he
pan
ts.
Pla
nL
et’s
mak
e a
list
sh
owin
g al
l po
ssib
le o
utc
omes
of
toss
ing
a co
in a
nd
then
spin
nin
g a
spin
ner
.
Sol
veH
�H
eads
T �
Tai
lsS
pin
ner
�1,
2,3
Th
ere
are
six
poss
ible
ou
tcom
es o
f fl
ippi
ng
a co
in a
nd
spin
nin
g a
spin
ner
.S
o,th
ere
are
6 di
ffer
ent
poss
ible
ou
tfit
s th
at R
icar
do c
an w
ear
for
the
firs
t da
yof
sch
ool.
Ch
eck
Fli
ppin
g a
coin
has
tw
o ou
tcom
es a
nd
ther
e ar
e tw
o sh
irts
.S
pin
nin
g a
thre
e-se
ctio
n s
pin
ner
has
th
ree
outc
omes
an
d th
ere
are
thre
e pa
irs
of p
ants
.T
her
efor
e,th
e so
luti
on o
f 6
diff
eren
t ou
tcom
es w
ith
a c
oin
an
d sp
inn
erre
pres
ent
the
6 po
ssib
le o
utf
it o
utc
omes
for
Ric
ardo
.
Fli
p a
Coi
nS
pin
a S
pin
ner
H1
H2
H3
T1
T2
T3
1.SC
IEN
CE
FAIR
Th
ere
are
4 st
ude
nts
wit
h p
roje
cts
to p
rese
nt
at t
he
sch
ool
scie
nce
fai
r.H
ow m
any
diff
eren
t w
ays
can
th
ese
4 pr
ojec
ts b
e di
spla
yed
on f
our
tabl
es i
n a
row
?24
way
s
2.G
END
ERD
eter
min
e w
het
her
fli
ppin
g a
coin
is
a go
od w
ay t
o pr
edic
t th
ege
nde
r of
th
e n
ext
5 ba
bies
bor
n a
t G
ener
al H
ospi
tal.
Just
ify
you
ran
swer
.N
o;
ther
e is
on
ly o
ne
scen
ario
in w
hic
h t
he
pre
dic
tio
n is
co
rrec
t.
3.O
LYM
PIC
SF
our
run
ner
s ar
e en
tere
d in
th
e fi
rst
hu
rdle
s h
eat
of t
wel
veh
eats
at
the
Oly
mpi
cs.
Th
e fi
rst
two
mov
e on
to
the
nex
t ro
un
d.A
ssu
min
g n
o ti
es,h
ow m
any
diff
eren
t w
ays
can
th
e fo
ur
run
ner
s co
me
infi
rst
and
seco
nd
plac
e?12
way
s
6SD
AP
3.2,
6S
DA
P2.
4St
udy
Guid
e an
d In
terv
entio
nP
rob
lem
-So
lvin
g In
vest
igat
ion
:A
ct It
Ou
t
Exer
cise
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
TI-8
3/84
Plu
s A
ctiv
ityC
om
bin
atio
ns
Cha
pter
940
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-5
A g
raph
ing
calc
ulat
or c
an b
e us
ed t
o so
lve
prob
lem
s in
volv
ing
com
bina
tion
s.O
n th
e T
I-83
/84
Plu
s,th
e co
mbi
nati
on f
unct
ion
can
be f
ound
in t
he M
ATH
(PRB
)men
u.
How
man
y w
ays
can
2 pe
ople
be
chos
en f
rom
a
grou
p of
10
peop
le?
Sin
ce o
rder
doe
s no
t mat
ter,
this
is a
com
bina
tion
.
Ent
er:
10
3 2
45
So,
the
num
ber
of w
ays
2 pe
ople
can
be
chos
en f
rom
a g
roup
of
10
peop
le is
45.
How
man
y 5-
card
han
ds c
an b
e ch
osen
fro
m a
de
ck o
f 52
car
ds?
Sin
ce o
rder
doe
s no
t mat
ter,
this
is a
com
bina
tion
.
Ent
er:
52
3 5
2,59
8,96
0
So,
the
num
ber
of 5
-car
d ha
nds
that
can
be
chos
en f
rom
a 5
2-ca
rd d
eck
is2,
598,
960.
Sol
ve e
ach
pro
ble
m.
1.H
ow m
any
grou
ps o
f 3
peop
le c
an b
e ch
osen
fro
m a
gro
up o
f 5
peop
le?
10
2.H
ow m
any
grou
ps o
f 4
peop
le c
an b
e ch
osen
fro
m a
gro
up o
f 8
peop
le?
70
3.H
ow m
any
grou
ps o
f 10
peo
ple
can
be c
hose
n fr
om a
gro
up o
f 20
peo
ple?
184,
756
4.H
ow m
any
grou
ps o
f 2
peop
le c
an b
e ch
osen
fro
m a
gro
up o
f 12
peo
ple?
66
5.H
ow m
any
grou
ps o
f 8
peop
le c
an b
e ch
osen
fro
m a
gro
up o
f 9
peop
le?
9
6.H
ow m
any
2-to
ppin
g pi
zzas
can
be
mad
e fr
om a
piz
za r
esta
uran
t of
feri
ng 6
dif
fere
nt
topp
ings
?15
7.H
ow m
any
3-to
ppin
g pi
zzas
can
be
mad
e fr
om a
piz
za r
esta
uran
t of
feri
ng 1
0 di
ffer
ent
topp
ings
?12
0
8.H
ow m
any
7-ca
rd h
ands
can
be
chos
en f
rom
a d
eck
of 5
2 ca
rds?
133,
784,
560
9.H
ow m
any
4-ca
rd h
ands
can
be
chos
en f
rom
a d
eck
of 5
2 ca
rds?
270,
725
10.
How
man
y tw
o-to
ppin
g su
ndae
s ca
n be
mad
e fr
om a
n ic
e cr
eam
sho
p of
feri
ng 9
dif
fere
nt
topp
ings
?36
EN
TER
MA
TH
EN
TER
MA
TH
Exam
ple
1
Exam
ple
2
Answers (Lessons 9-5 and 9-6)
Chapter 9 A17 Glencoe California Mathematics, Grade 6
Sele
ct t
he
Op
erat
ion
Mix
ed P
rob
lem
Sol
vin
g
For
Exe
rcis
es 1
an
d 2
,use
th
e ac
t it
ou
tst
rate
gy.
1.PO
P Q
UIZ
Use
th
e in
form
atio
n i
n t
he
tabl
e to
det
erm
ine
wh
eth
er t
ossi
ng
an
icke
l an
d a
dim
e is
a g
ood
way
to
answ
er a
5-q
ues
tion
mu
ltip
le-c
hoi
cequ
iz i
f ea
ch q
ues
tion
has
an
swer
ch
oice
sA
,B,C
,an
d D
.Ju
stif
y yo
ur
answ
er.
No
;S
amp
le a
nsw
er:T
he
exp
erim
ent
pro
du
ces
on
ly
1-2
corr
ect
answ
ers,
so
toss
ing
a n
icke
l an
d a
dim
e is
no
t a
go
od
way
to
an
swer
a
5-q
ues
tio
n m
ult
iple
-ch
oic
e q
uiz
.
2.B
OW
LIN
GB
ill,
Lu
cas,
Car
men
,an
dD
ena
go b
owli
ng
ever
y w
eek.
Wh
enor
dere
d fr
om h
igh
est
to l
owes
t,h
owm
any
way
s ca
n t
hei
r sc
ores
be
arra
nge
dif
Lu
cas
is n
ever
fir
st a
nd
Car
men
alw
ays
beat
s B
ill?
9
Use
an
y st
rate
gy t
o so
lve
Exe
rcis
es 3
and
4.S
ome
stra
tegi
es a
re s
how
n b
elow
.
3.B
OO
KS
Wh
at i
s th
e pr
obab
ilit
y of
fiv
ebo
oks
bein
g pl
aced
in
alp
hab
etic
al o
rder
of t
hei
r ti
tles
if
ran
dom
ly p
ut
on a
boo
ksh
elf?
4.N
UM
BER
TH
EORY
Th
e su
m o
f a
2-di
git
nu
mbe
r an
d th
e 2-
digi
t n
um
ber
wh
enth
e di
gits
are
rev
erse
d is
77.
If t
he
diff
eren
ce o
f th
e sa
me
two
nu
mbe
rs i
s45
,wh
at a
re t
he
two
2-di
git
nu
mbe
rs?
Th
e n
um
ber
s ar
e 61
an
d 1
6.
For
Exe
rcis
es 5
an
d 6
,sel
ect
the
app
rop
riat
e op
erat
ion
(s)
to s
olve
th
ep
rob
lem
s.J
ust
ify
you
r so
luti
on(s
) an
dso
lve
the
pro
ble
m.
5.B
ASE
BA
LLIn
on
e ga
me,
Raf
ael
was
up
toba
t 3
tim
es a
nd
mad
e 2
hit
s.In
an
oth
erga
me,
he
was
up
to b
at 5
tim
es w
ith
no
hit
s.W
hat
per
cen
t of
th
e ti
mes
at
bat
did
Raf
ael
mak
e a
hit
?A
dd
itio
n a
nd
div
isio
n;
2�
0�
2;3
�5
�8;
�2 8��
�1 4��
25%
6.R
ESTA
UR
AN
TA
res
tau
ran
t of
fers
th
epo
ssib
ilit
y of
168
th
ree-
cou
rse
din
ner
s.E
ach
din
ner
has
an
app
etiz
er,a
n e
ntr
ée,
and
a de
sser
t.If
th
e n
um
ber
ofap
peti
zers
dec
reas
es f
rom
7 t
o 5,
fin
dh
ow m
any
few
er p
ossi
ble
thre
e-co
urs
edi
nn
ers
the
rest
aura
nt
offe
rs.
Div
isio
n,m
ult
iplic
atio
n,a
nd
sub
trac
tio
n;
168
�7
�24
;24
�5
�12
0;16
8�
120
�48
;48
few
er p
oss
ible
din
ner
s
1� 12
0
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
943
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Lesson 9–6
pygp
9-6 P
RO
BL
EM
-SO
LVIN
G S
TR
AT
EG
IES
•U
se t
he fo
ur-s
tep
plan
.
•D
raw
a d
iagr
am.
•D
eter
min
e re
ason
able
ans
wer
s.
•A
ct it
out
.
Nic
kel
Dim
eA
nsw
er C
hoi
ceH
HA
HT
BT
HC
TT
D
6SD
AP
3.2,
6S
DA
P2.
4Pr
actic
eP
rob
lem
-So
lvin
g In
vest
igat
ion
:A
ct It
Ou
tU
se t
he
act
it o
ut
stra
tegy
to
solv
e.
1.SC
HO
OL
Det
erm
ine
wh
eth
er r
olli
ng
a 6-
side
d n
um
ber
cube
is
a go
od w
ayto
an
swer
a 2
0-qu
esti
on m
ult
iple
-ch
oice
tes
t if
th
ere
are
six
choi
ces
for
each
qu
esti
on.J
ust
ify
you
r an
swer
.N
o,y
ou
on
ly h
ave
a 1
in 6
chan
ce o
f g
etti
ng
th
e co
rrec
t an
swer
.
2.G
YM
NA
STIC
SF
ive
gym
nas
ts a
re e
nte
red
in a
com
peti
tion
.Ass
um
ing
that
ther
e ar
e n
o ti
es,h
ow m
any
way
s ca
n f
irst
,sec
ond,
and
thir
d pl
aces
be
awar
ded?
60
3.LU
NC
HH
ow m
any
way
s ca
n 3
fri
ends
sit
tog
eth
er i
n t
hre
e se
ats
at l
un
ch?
6
4.SC
HED
ULE
How
man
y di
ffer
ent
sch
edu
les
can
Sh
eila
cre
ate
if s
he
has
to
take
En
glis
h,m
ath
,sci
ence
,soc
ial
stu
dies
,an
d ar
t n
ext
sem
este
r.A
ssu
me
that
th
ere
is o
nly
on
e lu
nch
per
iod
avai
labl
e.12
0
5.B
AN
D C
ON
CER
TST
he
ban
d is
hav
ing
a h
olid
ay c
once
rt.I
n t
he
firs
t ro
w,
the
firs
t tr
um
pet
is a
lway
s fu
rth
est
to t
he
righ
t an
d th
e fi
rst
trom
bon
e is
alw
ays
the
furt
hes
t to
th
e le
ft.H
ow m
any
way
s ar
e th
ere
to a
rran
ge t
he
oth
er 4
peo
ple
wh
o n
eed
to s
it i
n t
he
fron
t? 24
6.TE
AM
SM
r.D
is
pick
ing
team
s fo
r vo
lley
ball
in
gym
by
hav
ing
the
stu
den
ts c
oun
t of
f by
2’s
.Th
e 1’
s w
ill
be o
n o
ne
team
an
d th
e 2’
s on
th
eot
her
.Wou
ld f
lipp
ing
a co
in w
ould
wor
k ju
st a
s w
ell
to p
ick
the
team
s?Ju
stif
y yo
ur
answ
er.
Ap
pro
xim
atel
y,ye
s;b
ecau
se t
he
pro
bab
ility
of
get
tin
g e
ith
er h
ead
s o
r ta
ils is
�1 2� ,th
e sa
me
asg
etti
ng
a o
ne
or
a tw
o.
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
942
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-6
6SD
AP
3.2,
6S
DA
P2.
4Sk
ills
Prac
tice
Pro
ble
m-S
olv
ing
Inve
stig
atio
n:
Act
it O
ut
Answers (Lesson 9-6)
Chapter 9 A18 Glencoe California Mathematics, Grade 6
An
swer
s
Get
Rea
dy
for
the
Less
on
Com
ple
te t
he
Min
i L
ab a
t th
e to
p o
f p
age
486
in y
our
text
boo
k.W
rite
you
r an
swer
s b
elow
.
1.C
ompa
re t
he
nu
mbe
r of
tim
es y
ou e
xpec
ted
to r
oll
a su
m o
f 7
wit
h t
he
nu
mbe
r of
tim
es y
ou a
ctu
ally
roll
ed a
su
m o
f 7.
Th
en c
ompa
re y
our
resu
ltto
th
e re
sult
s of
oth
er g
rou
ps.
See
stu
den
ts’w
ork
.
2.W
rite
th
e pr
obab
ilit
y of
rol
lin
g a
sum
of
7 ou
t of
36
roll
s u
sin
g th
en
um
ber
of t
imes
you
exp
ecte
dto
rol
l a
7 fr
om S
tep
1.T
hen
wri
te t
he
prob
abil
ity
of r
olli
ng
a su
m o
f 7
out
of 3
6 ro
lls
usi
ng
the
nu
mbe
r of
tim
esyo
u a
ctu
ally
roll
ed a
su
m o
f 7
from
Ste
p 2.
See
stu
den
ts’w
ork
.
Rea
d t
he
Less
on
3.L
ook
up
the
wor
d ex
peri
men
tal
in a
dic
tion
ary.
Wri
te t
he
mea
nin
g fo
r th
ew
ord
as u
sed
in t
he
less
on.
Sam
ple
an
swer
:b
ased
on
exp
erie
nce
rat
her
th
an o
n t
heo
ry
4.H
ow d
oes
theo
reti
cal
prob
abil
ity
diff
er f
rom
exp
erim
enta
l pr
obab
ilit
y?S
amp
le a
nsw
er:T
heo
reti
cal p
rob
abili
ty is
th
e ex
pec
ted
pro
bab
ility
of
an e
ven
t h
app
enin
g.E
xper
imen
tal p
rob
abili
tyis
bas
ed o
n s
om
eth
ing
yo
u a
ctu
ally
try
(fo
r ex
amp
le,a
nex
per
imen
t o
r g
ame)
.5.
Com
plet
e th
e se
nte
nce
:Exp
erim
enta
l pr
obab
ilit
y ca
n b
e ba
sed
onp
ast
per
form
ance
san
d ca
n b
e u
sed
to m
ake
pred
icti
ons
abou
t fu
ture
even
ts.
Rem
emb
er W
hat
Yo
u L
earn
ed6.
Wor
k w
ith
a p
artn
er.D
esig
n a
n e
xper
imen
t th
at y
ou c
an u
se t
o ex
pres
sth
e ex
peri
men
tal
prob
abil
ity
of a
n e
ven
t.C
ompa
re y
our
fin
din
gs w
ith
thos
e of
oth
ers
in y
our
clas
s.S
ee s
tud
ents
’wo
rk.
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
945
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
pygp
9-7
Lesson 9–7
6SD
AP
3.2
Less
on R
eadi
ng G
uide
T
heo
reti
cal a
nd
Exp
erim
enta
l Pro
bab
ility
Sol
ve e
ach
pro
ble
m u
sin
g an
y st
rate
gy y
ou h
ave
lear
ned
.
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
944
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-6
3.B
ASE
BA
LLT
hir
ty-t
wo
team
s ar
e pl
ayin
gin
th
e ch
ampi
onsh
ip.I
f a
team
is
elim
inat
ed o
nce
it
lose
s,h
ow m
any
tota
l ga
mes
wil
l be
pla
yed
in t
he
cham
pion
ship
?31
4.G
EOM
ETRY
Fin
d th
e n
ext
two
term
s in
the
sequ
ence
.
5.PO
OL
REN
TAL
Th
e ta
ble
belo
w s
how
sh
ow m
uch
For
d M
iddl
e S
choo
l w
asch
arge
d to
ren
t th
e po
ol f
or a
par
tyba
sed
on t
he
nu
mbe
r of
hou
rs i
t w
asre
nte
d.P
redi
ct t
he
cost
for
5 h
ours
.$6
00
6.G
EOM
ETRY
Use
th
e fo
rmu
la D
�rt
wh
ere
Dis
th
e di
stan
ce,r
is t
he
rate
,an
d t
is t
he
tim
e to
det
erm
ine
how
far
Aly
ssa
drov
e if
sh
e dr
ove
55 m
iles
per
hou
r fo
r 4
hou
rs.
220
mile
s
7.SC
HO
OL
ELEC
TIO
NS
How
man
y w
ays
can
a p
resi
den
t,vi
ce p
resi
den
t,se
cret
ary
and
trea
sure
r be
ele
cted
fr
om a
ch
oice
of
6 st
ude
nts
?36
0
8.SH
OPP
ING
Mor
ty b
ough
t sk
is.T
he
skis
cost
$21
5 an
d h
e go
t $3
5 in
ch
ange
.H
ow m
uch
did
Mor
ty p
ay w
ith
?$2
50
# of
hou
rsC
ost
1$1
201.
5$1
802
$240
2.5
$300
An
swer
:
1.PO
LLS
Ou
t of
200
peo
ple,
32%
sai
d th
atth
eir
favo
rite
an
imal
was
a c
at a
nd
44%
sai
d th
at t
hei
r fa
vori
te a
nim
al w
asa
dog.
How
man
y m
ore
peop
le c
hos
edo
g th
an c
at?
24
2.PE
AC
HES
Roi
is
pick
ing
peac
hes
He
nee
ds a
tot
al o
f 3�
1 2�bu
shel
s of
pea
ches
.
If h
e h
as a
lrea
dy p
icke
d 3
bush
els,
how
man
y m
ore
does
he
nee
d to
pic
k?B
A2
bush
els
C3�
1 2�bu
shel
s
B�1 2�
bush
elD
3 bu
shel
s
6SD
AP
3.2,
6S
DA
P2.
4W
ord
Prob
lem
Pra
ctic
eP
rob
lem
-So
lvin
g In
vest
igat
ion
:A
ct It
Ou
t
Answers (Lessons 9-6 and 9-7)
Chapter 9 A19 Glencoe California Mathematics, Grade 6
For
Exe
rcis
es 1
–5,a
nu
mb
er c
ub
e is
rol
led
50
tim
es a
nd
th
e re
sult
sar
e sh
own
in
th
e gr
aph
bel
ow.
1.F
ind
the
expe
rim
enta
l pr
obab
ilit
y of
rol
lin
g a
2.� 24 5�
2.W
hat
is
the
theo
reti
cal
prob
abil
ity
of r
olli
ng
a 2?
�1 6�
3.F
ind
the
expe
rim
enta
l pr
obab
ilit
y of
not
roll
ing
a 2.
�2 21 5�
4.W
hat
is
the
theo
reti
cal
prob
abil
ity
of n
otro
llin
g a
2?�5 6�
5.F
ind
the
expe
rim
enta
l pr
obab
ilit
y of
rol
lin
g a
1.�1 5�
For
Exe
rcis
es 6
–9,u
se t
he
resu
lts
of t
he
surv
ey a
t th
e ri
ght.
6.W
hat
is
the
prob
abil
ity
that
a p
erso
n’s
fa
vori
te s
easo
n i
s fa
ll?
Wri
te t
he
prob
abil
ity
as a
fra
ctio
n.
�1 4�
7.O
ut
of 3
00 p
eopl
e,h
ow m
any
wou
ld y
ou
expe
ct t
o sa
y th
at f
all
is t
hei
r fa
vori
te s
easo
n?
75
8.O
ut
of 2
0 pe
ople
,how
man
y w
ould
you
exp
ect
to s
ay t
hat
th
ey l
ike
all
the
seas
ons?
2
9.O
ut
of 6
50 p
eopl
e,h
ow m
any
mor
e w
ould
you
exp
ect
to s
ay t
hat
th
ey l
ike
sum
mer
th
an s
ay t
hat
th
ey l
ike
win
ter?
169
Sprin
g
Sum
mer
Fall
Win
ter
Non
e, I
like
them
all
13%
39%
25%
13%
10%
Wha
t is
your
favo
rite
seas
on o
f the
yea
r?
63
21
81012 4614 02
Number of Rolls
54
108
6
9
5
12
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
947
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Lesson 9–7
pygp
9-7
6SD
AP
3.2
Skill
s Pr
actic
eT
heo
reti
cal a
nd
Exp
erim
enta
l Pro
bab
ility
Exer
cise
s
Th
e gr
aph
sh
ows
the
resu
lts
of a
n
exp
erim
ent
in w
hic
h a
nu
mb
ercu
be
was
rol
led
100
tim
es.F
ind
th
e ex
per
imen
tal
pro
bab
ilit
y of
rol
lin
g a
3 fo
r th
is e
xper
imen
t.
P(3
) �
� � 11 06 0�
or � 24 5�
Th
e ex
peri
men
tal
prob
abil
ity
of r
olli
ng
a 3
is � 24 5�
,wh
ich
is
clos
e to
its
th
eore
tica
l
prob
abil
ityo
f �1 6�.
In a
tel
eph
one
pol
l,22
5 p
eop
le w
ere
ask
ed
for
wh
om t
hey
pla
nn
ed t
o vo
te i
n t
he
race
fo
r m
ayor
.Wh
at i
s th
e ex
per
imen
tal
pro
bab
ilit
y of
J
uar
ez b
ein
g el
ecte
d?
Of
the
225
peop
le p
olle
d,75
pla
nn
ed t
o vo
te f
or J
uar
ez.
So,
the
expe
rim
enta
l pr
obab
ilit
y is
� 27 25 5�or
�1 3�.
Su
pp
ose
5,70
0 p
eop
le v
ote
in t
he
elec
tion
.H
ow m
any
can
be
exp
ecte
d t
o vo
te f
or J
uar
ez?
�1 3��
5,70
0 �
1,9
00
Abo
ut
1,90
0 w
ill
vote
for
Ju
arez
.
For
Exe
rcis
es 1
–3,u
se t
he
grap
h o
f a
surv
ey o
f 15
0 st
ud
ents
ask
ed w
het
her
th
ey p
refe
r ca
ts o
r d
ogs.
1.W
hat
is
the
prob
abil
ity
of a
stu
den
t pr
efer
rin
g do
gs?
�2 22 5�
2.S
upp
ose
100
stu
den
ts w
ere
surv
eyed
.How
man
y ca
n b
e ex
pect
ed t
o pr
efer
dog
s?88
3.S
upp
ose
300
stu
den
ts w
ere
surv
eyed
.How
man
y ca
n b
e ex
pect
ed t
o pr
efer
cat
s?36
Dog
sC
ats
6080100 40 020120
140
Number of Students
18
132
nu
mbe
r of
tim
es 3
occ
urs
��
��
nu
mbe
r of
pos
sibl
e ou
tcom
es6
32
1
20 101525 05
Number of Rolls
54
1413
1619
2117
Num
ber S
how
ing
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
946
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-7
Exp
erim
enta
l pro
bab
ility
is fo
und
usin
g fr
eque
ncie
s ob
tain
ed in
an
expe
rimen
t or
gam
e.T
heo
reti
cal
pro
bab
ility
is t
he e
xpec
ted
prob
abili
ty o
f an
eve
nt o
ccur
ring.
Can
did
ate
Nu
mb
er o
fP
eop
leJu
arez
75D
avis
67A
bram
son
83
Exam
ple
1
Exam
ple
2
Exam
ple
3
6SD
AP
3.2
Stud
y Gu
ide
and
Inte
rven
tion
Th
eore
tica
l an
d E
xper
imen
tal P
rob
abili
ty
Answers (Lesson 9-7)
Chapter 9 A20 Glencoe California Mathematics, Grade 6
An
swer
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
949
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Lesson 9–7
pygp
9-7
HO
BB
IES
For
Exe
rcis
es 1
–3,u
se t
he
WIN
TER
AC
TIV
ITIE
SF
or E
xerc
ises
5 a
nd
6,
grap
h o
f a
surv
ey o
f 24
sev
enth
gra
de
use
th
e gr
aph
of
a su
rvey
wit
h 1
04st
ud
ents
ask
ed t
o n
ame
thei
r fa
vori
te
resp
onse
s in
wh
ich
res
pon
den
ts w
ere
hob
by
.as
ked
ab
out
thei
r fa
vori
te w
inte
r ac
tivi
ties
.
1020
3040
5060
700
Bui
ldin
g a
snow
man
Snow
boar
ding
/ski
ing
Sled
ding
Wha
t is
your
favo
rite
win
ter
activ
ity?
1469
21 Resp
onde
nts
24
68
1012
140
Sing
ing
Han
ging
with
frie
nds
Bui
ldin
g th
ings
Bik
e rid
ing
T.V.
Com
pute
rRo
ller
skat
ing
Spor
tsWha
t is
your
favo
rite
hob
by?
13
12
3 3 38
Num
ber o
f Stu
dent
s
1.W
hat
is
the
prob
abil
ity
that
a s
tude
nt’s
favo
rite
hob
by i
s ro
ller
ska
tin
g?
�1 8�
2.S
upp
ose
200
seve
nth
gra
de s
tude
nts
wer
e su
rvey
ed.H
ow m
any
can
be
expe
cted
to
say
that
rol
ler
skat
ing
isth
eir
favo
rite
hob
by?
25
3.S
upp
ose
60 s
even
th g
rade
stu
den
tsw
ere
surv
eyed
.How
man
y ca
n b
eex
pect
ed t
o sa
y th
at b
ike
ridi
ng
is t
hei
rfa
vori
te h
obby
?5
4.M
AR
BLE
SA
bag
con
tain
s 5
blu
e,4
red,
9 w
hit
e,an
d 6
gree
n m
arbl
es.I
f a
mar
ble
is d
raw
n a
t ra
ndo
m a
nd
repl
aced
100
tim
es,h
ow m
any
tim
esw
ould
you
exp
ect
to d
raw
a g
reen
mar
ble?
25
5.W
hat
is
the
prob
abil
ity
that
som
eon
e’s
favo
rite
win
ter
acti
vity
is
buil
din
g a
snow
man
? W
rite
th
e pr
obab
ilit
y as
afr
acti
on.
� 57 2�
6.If
500
peo
ple
had
res
pon
ded,
how
man
yw
ould
hav
e be
en e
xpec
ted
to l
ist
sled
din
g as
th
eir
favo
rite
win
ter
acti
vity
? R
oun
d to
th
e n
eare
st w
hol
epe
rson
.10
1
6SD
AP
3.2
Wor
d Pr
oble
m P
ract
ice
Th
eore
tica
l an
d E
xper
imen
tal P
rob
abili
tyF
or E
xerc
ises
1–4
,a n
um
ber
cu
be
is r
olle
d 2
4 ti
mes
an
d l
and
s on
2fo
ur
tim
es a
nd
on
6 t
hre
e ti
mes
.
1.F
ind
the
expe
rim
enta
l pr
obab
ilit
y of
lan
din
g on
a 2
.�1 6�
2.F
ind
the
expe
rim
enta
l pr
obab
ilit
y of
not
lan
din
g on
a 6
.�7 8�
3.C
ompa
re t
he
expe
rim
enta
l pr
obab
ilit
y yo
u f
oun
d in
Exe
rcis
e 1
to i
tsth
eore
tica
l pr
obab
ilit
y.T
he
theo
reti
cal p
rob
abili
ty o
f la
nd
ing
on
a 2,
�1 6� ,is
th
e sa
me
as t
he
exp
erim
enta
l pro
bab
ility
.
4.C
ompa
re t
he
expe
rim
enta
l pr
obab
ilit
y yo
u f
oun
d in
Exe
rcis
e 2
to i
tsth
eore
tica
l pr
obab
ilit
y.T
he
theo
reti
cal p
rob
abili
ty o
f n
ot
lan
din
g
on
a 6
,�5 6�
,is
fair
ly c
lose
to
th
e ex
per
imen
tal p
rob
abili
ty.
ENTE
RTA
INM
ENT
For
Exe
rcis
es 5
–7,u
se t
he
resu
lts
of t
he
surv
ey
in t
he
tab
le s
how
n.
5.W
hat
is
the
prob
abil
ity
that
som
eon
ein
th
e su
rvey
con
side
red
read
ing
book
s or
su
rfin
g th
e In
tern
et a
s th
ebe
st e
nte
rtai
nm
ent
valu
e? W
rite
th
epr
obab
ilit
y as
a f
ract
ion
.� 13 01 0�
6.O
ut
of 5
00 p
eopl
e su
rvey
ed,h
ow m
any
wou
ld y
ou e
xpec
t co
nsi
dere
d re
adin
gbo
oks
or s
urf
ing
the
Inte
rnet
as
the
best
en
tert
ain
men
t va
lue?
155
7.O
ut
of 3
00 p
eopl
e su
rvey
ed,i
s it
reas
onab
le t
o ex
pect
th
at 3
0co
nsi
dere
d w
atch
ing
tele
visi
on a
s th
ebe
st e
nte
rtai
nm
ent
valu
e? W
hy
or w
hy
not
? N
o;
1% o
f 30
0 =
3,n
ot
30.
For
Exe
rcis
es 8
–10,
a sp
inn
er m
ark
ed w
ith
fou
r se
ctio
ns
blu
e,gr
een
,ye
llow
,an
d r
ed w
as s
pu
n 1
00 t
imes
.Th
e re
sult
s ar
e sh
own
in
th
e ta
ble
.
8.F
ind
the
expe
rim
enta
l pr
obab
ilit
y of
lan
din
g on
gre
en.
� 11 0�
9.F
ind
the
expe
rim
enta
l pr
obab
ilit
y of
lan
din
g on
red
.�1 27 5�
10.
If t
he
spin
ner
is
spu
n 5
0 m
ore
tim
es,
how
man
y of
th
ese
tim
es w
ould
you
ex
pect
th
e po
inte
r to
lan
d on
blu
e?7
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
948
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-7
Sec
tion
Fre
qu
ency
Blu
e14
Gre
en10
Yell
ow8
Red
68
Bes
t E
nte
rtai
nm
ent
Val
ue
Typ
e of
En
tert
ain
men
tP
erce
nt
Pla
yin
g In
tera
ctiv
e G
ames
48%
Rea
din
g B
ooks
22%
Ren
tin
g M
ovie
s10
%G
oin
g to
Mov
ie T
hea
ters
10%
Su
rfin
g th
e In
tern
et9%
Wat
chin
g T
elev
isio
n1%
6SD
AP
3.2
Prac
tice
Th
eore
tica
l an
d E
xper
imen
tal P
rob
abili
ty
Answers (Lesson 9-7)
Chapter 9 A21 Glencoe California Mathematics, Grade 6
Exer
cise
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
TI-7
3 A
ctiv
ityE
xper
imen
tal P
rob
abili
ty
Cha
pter
951
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Lesson 9–7
pygp
9-7
Use
you
r ca
lcul
ator
to
sim
ulat
e fl
ippi
ng a
coi
n or
rol
ling
a nu
mbe
r cu
be.T
hese
fea
ture
s ar
efo
und
in t
he M
ATH
PRB
(pro
babi
lity)
men
u.T
he c
alcu
lato
r di
spla
ys a
ran
dom
num
ber
that
repr
esen
ts h
eads
or
tails
on
a co
in o
r th
e nu
mbe
r on
a n
umbe
r cu
be.T
he c
alcu
lato
r ca
llsnu
mbe
r cu
bes
dice
. Rol
l tw
o nu
mbe
r cu
bes
100
tim
es.C
alcu
late
the
exp
erim
enta
l pro
babi
lity
ofro
lling
dou
ble-
1,do
uble
-2,d
oubl
e-3,
doub
le-4
,dou
ble-
5,or
dou
ble-
6.
Step
1C
lear
Hom
e.St
ep 2
Cho
ose
the
dice
fea
ture
in M
ATH
PRB.
[MEM
]5
7
Step
3T
he d
ispl
ay s
how
s di
ce(.
Use
2 d
ice.
Step
4In
terp
ret t
he r
esul
t and
con
tinu
e fo
r
210
0 ro
lls.
The
dis
play
sho
ws
an o
rder
ed p
air
of d
igits
, lik
e (3
5).
Thi
s m
eans
the
firs
t cub
e sh
ows
a 3
and
the
seco
nd c
ube
show
s a
5. I
f a
doub
le, l
ike
(2 2
) or
(5
5),
app
ears
, tal
ly it
in th
e ch
art b
elow
. Con
tinue
w
ith
the
next
rol
l by
pres
sing
.
Use
you
r gr
aph
ing
calc
ula
tor
to c
omp
lete
th
e fo
llow
ing.
1.C
ompl
ete
the
tabl
e fo
r 10
0 ro
lls.
Cal
cula
te th
e Fr
actio
n an
d Pe
rcen
tco
lum
ns.
See
sam
ple
dat
a.2.
The
theo
reti
cal p
roba
bili
ty o
fro
llin
g do
uble
-1 (
or a
ny o
ther
doub
le)
is 1
/36
or a
bout
3%
.C
ompa
re th
is th
eore
tica
lpr
obab
ilit
y w
ith
your
expe
rim
enta
l res
ults
.M
ost
of
the
exp
erim
enta
lp
rob
abili
ties
are
clo
se t
oth
e th
eore
tica
l.3.
Do
anot
her
expe
rim
ent,
but u
se th
e co
in f
eatu
re o
f M
ATH
PRB.
Exp
lore
the
prob
abil
ity
of a
fam
ily w
ith
thre
e ch
ildr
en h
avin
g al
l gir
ls. F
lip
3 co
ins.
Eac
h co
in s
tand
s fo
r on
e ch
ild.
If
the
resu
lt is
a 1
, the
n th
e ch
ild
is a
boy
; if
it is
0, t
hen
the
chil
d is
a g
irl.
Fli
p th
e th
ree
coin
s 10
0 ti
mes
. Tal
ly th
e re
sult
s of
3 g
irls
and
of
3 bo
ys. D
escr
ibe
your
res
ults
.
EN
TE
R
EN
TE
R
MA
TH
EN
TE
R2n
d
Dou
ble
Tal
lyN
umbe
rF
ract
ion
Per
cent
(1, 1
)||
2� 12 00�
2%
(2, 2
)|||
|4
� 14 00�4%
(3, 3
)||
2� 12 00�
2%
(4, 4
)|||
|4
� 14 00�4%
(5, 5
)|||
| ||
7� 17 00�
7%
(6, 6
)|||
3� 13 00�
3%
Tal
lyN
umbe
rF
ract
ion
Per
cent
All
gir
ls (
0, 0
, 0)
|||| |
||| |
11� 11 01 0�
11%
All
boy
s (1
, 1, 1
)|||
| ||||
10� 11 00 0�
10%
Exam
ple
1
Stu
den
ts’r
esu
lts
and
des
crip
tio
ns
will
var
y.
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Enri
chm
ent
Cha
pter
950
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-7
Ro
llin
g a
Do
dec
ahed
ron
A d
odec
ahed
ron
is a
sol
id.I
t h
as t
wel
ve f
aces
,an
d ea
ch f
ace
is a
pen
tago
n.
At
the
righ
t,yo
u s
ee a
dod
ecah
edro
n w
hos
e fa
ces
are
mar
ked
wit
h
the
inte
gers
fro
m 1
th
rou
gh 1
2.Yo
u c
an r
oll
this
dod
ecah
edro
n ju
st
as y
ou r
oll
a n
um
ber
cube
.Wit
h t
he
dode
cah
edro
n,h
owev
er,t
her
e ar
e tw
elve
equ
ally
lik
ely
outc
omes
.
Ref
er t
o th
e d
odec
ahed
ron
sh
own
at
the
righ
t.F
ind
th
e p
rob
abil
ity
of e
ach
eve
nt.
1.P
(5)
� 11 2�2.
P(o
dd)
�1 2�
3.P
(pri
me)
� 15 2�4.
P(d
ivis
ible
by
5)�1 6�
5.P
(les
s th
an 4
)�1 4�
6.P
(fra
ctio
n)
0
You
can
mak
e yo
ur
own
dod
ecah
edro
n b
y cu
ttin
g ou
t th
e pa
tter
n a
t th
e ri
ght.
Fol
d al
ong
each
of
the
soli
d li
nes
.Th
en u
se t
ape
to jo
in t
he
face
s to
geth
er s
o th
at
you
r do
deca
hed
ron
loo
ks l
ike
the
one
show
n a
bove
.
7.R
oll
you
r do
deca
hed
ron
100
tim
es.R
ecor
d yo
ur
resu
lts
on a
sep
arat
e sh
eet
of p
aper
,usi
ng
a ta
ble
like
th
is.
An
swer
s w
ill v
ary.
8.U
se y
our
resu
lts
from
Exe
rcis
e 7.
Fin
d th
e ex
peri
men
tal
prob
abil
ity
for
each
of
the
even
ts
desc
ribe
d in
Exe
rcis
es 1
–6.
An
swer
s w
ill v
ary.
Outc
ome
1 2
Tally
Freq
uenc
y
1
2
3
4 5
6
7
11
12
8
9
10
2
1110
1
36
6SD
AP
3.2
Answers (Lesson 9-7)
Chapter 9 A22 Glencoe California Mathematics, Grade 6
An
swer
s
Exer
cise
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Co
mp
ou
nd
Eve
nts
Cha
pter
953
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Lesson 9–8
pygp
9-8
A c
oin
is
toss
ed a
nd
a n
um
ber
cu
be
is r
olle
d.F
ind
th
e p
rob
abil
ity
of t
ossi
ng
tail
s an
d r
olli
ng
a 5.
P(t
ails
) �
�1 2�P
(5)
��1 6�
P(t
ails
an
d 5)
��1 2�
��1 6�
or � 11 2�
So,
the
prob
abil
ity
of t
ossi
ng
tail
s an
d ro
llin
g a
5 is
� 11 2�.
MA
RB
LES
A b
ag c
onta
ins
7 b
lue,
3 gr
een
,an
d 3
red
mar
ble
s.If
Agn
es
ran
dom
ly d
raw
s tw
o m
arb
les
from
th
e b
ag,r
epla
cin
g th
e fi
rst
bef
ore
dra
win
g th
e se
con
d,w
hat
is
the
pro
bab
ilit
y of
dra
win
g a
gree
n a
nd
th
en a
blu
e m
arb
le?
P(g
reen
) �
3/13
1 13
mar
bles
, 3
are
gree
n
P(b
lue)
�7/
13
13 m
arbl
es,
7 ar
e bl
ue
P(g
reen
,th
en b
lue)
�� 13 3�
· �17 2�
�� 12 61 9�
So,
the
prob
abil
ity
that
Agn
es w
ill
draw
a g
reen
,th
en a
blu
e m
arbl
e is
� 12 61 9�.
1.F
ind
the
prob
abil
ity
of r
olli
ng
a 2
and
then
an
eve
n n
um
ber
on t
wo
con
secu
tive
rol
ls o
f a
nu
mbe
r cu
be.
� 11 2�
2.A
pen
ny
and
a di
me
are
toss
ed.W
hat
is
the
prob
abil
ity
that
th
e pe
nn
yla
nds
on
hea
ds a
nd
the
dim
e la
nds
on
tai
ls?
�1 4�
3.L
azlo
’s s
ock
draw
er c
onta
ins
8 bl
ue
and
5 bl
ack
sock
s.If
he
ran
dom
lypu
lls
out
one
sock
,wh
at i
s th
e pr
obab
ilit
y th
at h
e pi
cks
a bl
ue
sock
?
� 18 3�
A c
om
po
un
d e
ven
tco
nsis
ts o
f tw
o or
mor
e si
mpl
e ev
ents
.If
the
outc
ome
of o
ne e
vent
doe
s no
t af
fect
the
outc
ome
of a
sec
ond
even
t, th
e ev
ents
are
cal
led
ind
epen
den
t ev
ents
.The
pro
babi
lity
of t
wo
inde
pend
ent
even
ts c
an b
e fo
und
by m
ultip
lyin
g th
e pr
obab
ility
of
the
first
eve
nt b
y th
e pr
obab
ility
of
the
seco
nd e
vent
.
Exam
ple
1
Exam
ple
2
6SD
AP
3.4,
6S
DA
P3.
5
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Less
on R
eadi
ng G
uide
Co
mp
ou
nd
Eve
nts
Cha
pter
952
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-8
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n a
t th
e to
p o
f p
age
492
in y
our
text
boo
k.W
rite
you
r an
swer
s b
elow
.
1.W
hat
is
the
prob
abil
ity
of O
mar
bei
ng
in t
he
seco
nd
hea
t? i
n L
ane
3?�1 4�;
�1 5�
2.M
ult
iply
you
r an
swer
s in
Exe
rcis
es 1
.Wh
at d
oes
this
nu
mbe
r re
pres
ent?
� 21 0�;
the
pro
bab
ility
of
Om
ar b
ein
g in
lan
e 3
of
the
seco
nd
hea
t
Rea
d t
he
Less
on
Use
th
e in
trod
uct
ion
to
the
less
on t
o an
swer
Exe
rcis
es 4
–6.
3.W
hat
doe
s a
com
pou
nd
even
t co
nsi
st o
f?It
co
nsi
sts
of
two
or
mo
resi
mp
le e
ven
ts.
4.D
efin
e in
depe
nde
nt
even
ts.
Th
ey a
re t
wo
eve
nts
in w
hic
h t
he
ou
tco
me
of
on
e,d
oes
no
t af
fect
th
e o
utc
om
e o
f th
e o
ther
.
5.W
rite
th
e pr
obab
ilit
y of
in
depe
nde
nt
even
ts i
n s
ymbo
ls.
P(A
an
d B
) �
P(A
) �
P(B
)
6.H
ow c
an y
ou f
ind
the
prob
abil
ity
of t
wo
inde
pen
den
t ev
ents
?S
amp
lean
swer
:M
ult
iply
th
e p
rob
abili
ty o
f th
e fi
rst
even
t by
th
ep
rob
abili
ty o
f th
e se
con
d e
ven
t.
Rem
emb
er W
hat
Yo
u L
earn
ed7.
Lis
t se
vera
l in
depe
nde
nt
com
pou
nd
even
ts.E
xpla
in w
hy
you
con
side
r th
eev
ents
to
be i
nde
pen
den
t.S
amp
le a
nsw
er:
spin
nn
ing
a s
pin
ner
and
flip
pin
g a
co
in.T
hey
hav
e n
o e
ffec
t o
n e
ach
oth
er.6S
DA
P3.
4, 6
SD
AP
3.5
Answers (Lesson 9-8)
Chapter 9 A23 Glencoe California Mathematics, Grade 6
A n
um
ber
cu
be
is r
olle
d a
nd
a s
pin
ner
lik
e th
e on
e sh
own
is
spu
n.
Fin
d e
ach
pro
bab
ilit
y.
1.P
(6 a
nd
D)
� 21 4�2.
P(m
ult
iple
of
2 an
d B
)�1 8�
3.P
(not
6 a
nd
not
A)
�5 8�
A s
et o
f 7
card
s is
lab
eled
1–7
.A s
econ
d s
et o
f 12
car
ds
con
tain
s th
e fo
llow
ing
colo
rs:3
gre
en,6
red
,2 b
lue,
and
1 w
hit
e.O
ne
card
fro
m e
ach
set
is
sele
cted
.Fin
dea
ch p
rob
abil
ity.
4.P
(6 a
nd
gree
n)
� 21 8�5.
P(p
rim
e an
d bl
ue)
� 22 1�6.
P(o
dd a
nd
red)
�2 7�
7.P
(7 a
nd
wh
ite)
� 81 4�8.
P(m
ulti
ple
of 3
and
red
)�1 7�
9.P
(eve
n a
nd
wh
ite)
� 21 8�
A c
oin
is
toss
ed,a
nu
mb
er c
ub
e is
rol
led
,an
d a
let
ter
is p
ick
ed f
rom
the
wor
d f
ram
er.
10.
P(t
ails
,5,m
)� 71 2�
11.
P(h
eads
,odd
,r)
� 11 2�12
.P
(hea
ds,6
,vow
el)
� 31 6�
13.
P(t
ails
,pri
me,
cons
onan
t)14
.P
(not
tai
ls,m
ulti
ple
of 3
,a)
15.
P(n
ot h
eads
,2,f
)� 71 2�
�1 6�� 31 6�
16.
TOLL
RO
AD
Mr.
Esp
inoz
a ra
ndo
mly
ch
oose
s on
e of
fiv
e to
ll b
ooth
s w
hen
ente
rin
g a
toll
roa
d w
hen
dri
vin
g to
wor
k.W
hat
is
the
prob
abil
ity
he
wil
lse
lect
th
e m
iddl
e to
ll b
ooth
on
Mon
day
and
Tu
esda
y?� 21 5�
MA
RB
LES
For
Exe
rcis
es 1
7–20
,use
th
ein
form
atio
n i
n t
he
tab
le s
how
n t
o fi
nd
eac
hp
rob
abil
ity.
Aft
er a
mar
ble
is
ran
dom
ly p
ick
edfr
om a
bag
con
tain
ing
mar
ble
s of
fou
r d
iffe
ren
tco
lors
,th
e co
lor
of t
he
mar
ble
is
obse
rved
an
dth
en i
t is
ret
urn
ed t
o th
e b
ag.
17.
P(r
ed)
� 11 2�18
.P
(gre
en,b
lue)
� 21 4�
19.
P(r
ed,w
hit
e,bl
ue)
� 91 6�20
.P
(blu
e,bl
ue,
blu
e)� 61 4�
A D
CB
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Prac
tice
Co
mp
ou
nd
Eve
nts
Cha
pter
955
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Lesson 9–8
pygp
9-8
Mar
ble
sC
olor
Nu
mb
erW
hit
e6
Gre
en2
Red
1B
lue
3
6SD
AP
3.4,
6S
DA
P3.
5
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Skill
s Pr
actic
eC
om
po
un
d E
ven
ts
Cha
pter
954
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-8
1.F
our
coin
s ar
e to
ssed
.Wh
at i
s th
e pr
obab
ilit
y of
tos
sin
g al
l h
eads
?
� 11 6�
2.O
ne
lett
er i
s ra
ndo
mly
sel
ecte
d fr
om t
he
wor
d P
RIM
E a
nd
one
lett
er i
sra
ndo
mly
sel
ecte
d fr
om t
he
wor
d M
AT
H.W
hat
is
the
prob
abil
ity
that
both
let
ters
sel
ecte
d ar
e vo
wel
s?
� 11 0�
3.A
car
d is
ch
osen
at
ran
dom
fro
m a
dec
k of
52
card
s.It
is
then
rep
lace
dan
d a
seco
nd
card
is
chos
en.W
hat
is
the
prob
abil
ity
of g
etti
ng
a ja
ck a
nd
then
an
eig
ht?
� 11 69�
For
Exe
rcis
es 4
–6,u
se t
he
info
rmat
ion
bel
ow.
A s
tan
dard
dec
k of
pla
yin
g ca
rds
con
tain
s 52
car
ds i
n f
our
suit
s of
13
card
sea
ch.T
wo
suit
s ar
e re
d an
d tw
o su
its
are
blac
k.F
ind
each
pro
babi
lity
.Ass
um
eth
e fi
rst
card
is
repl
aced
bef
ore
the
seco
nd
card
is
draw
n.
4.P
(bla
ck,q
uee
n)
5.P
(bla
ck,d
iam
ond)
6.P
(jac
k,qu
een
)
� 21 6��1 8�
� 11 69�
7.W
hat
is
the
prob
abil
ity
of s
pin
nin
g a
nu
mbe
r gr
eate
r th
an 5
on
a s
pin
ner
nu
mbe
red
1 to
8 a
nd
toss
ing
a ta
il o
n a
coi
n?
� 13 6�
8.T
wo
card
s ar
e ch
osen
at
ran
dom
fro
m a
sta
nda
rd d
eck
of c
ards
wit
hre
plac
emen
t.W
hat
is
the
prob
abil
ity
of g
etti
ng
2 ac
es?
� 11 69�
9.A
CD
rac
k h
as 8
cla
ssic
al C
Ds,
5 po
p C
Ds,
and
3 ro
ck C
Ds.
On
e C
D i
sch
osen
an
d re
plac
ed,t
hen
a s
econ
d C
D i
s ch
osen
.Wh
at i
s th
e pr
obab
ilit
yof
ch
oosi
ng
a ro
ck C
D t
hen
a c
lass
ical
CD
?
� 33 2�
10.
A ja
r h
olds
15
red
pen
cils
an
d 10
blu
e pe
nci
ls.W
hat
is
the
prob
abil
ity
ofdr
awin
g on
e re
d pe
nci
l fr
om t
he
jar?
�3 5�
6SD
AP
3.4,
6S
DA
P3.
5
Answers (Lesson 9-8)
Chapter 9 A24 Glencoe California Mathematics, Grade 6
An
swer
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Enri
chm
ent
Cha
pter
957
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Lesson 9–8
pygp
9-8
Co
mp
ou
nd
Eve
nts
Th
e ga
me
of r
oule
tte
is p
laye
d by
dro
ppin
g a
ball
into
a s
pin
nin
g,bo
wl-
shap
ed w
hee
l.W
hen
th
ew
hee
l st
ops
spin
nin
g,th
e ba
ll w
ill
com
e to
res
t in
any
of 3
8 lo
cati
ons.
On
a r
oule
tte
wh
eel,
the
eigh
teen
eve
n n
um
bers
from
2 t
hro
ugh
36
are
colo
red
red
and
the
eigh
teen
odd
nu
mbe
rs f
rom
1 t
hro
ugh
35
are
colo
red
blac
k.T
he
nu
mbe
rs 0
an
d 00
are
col
ored
gree
n.
To
fin
d th
e pr
obab
ilit
y of
tw
o in
depe
nde
nt
even
ts,
the
resu
lts
of t
wo
spin
s,fi
nd
the
prob
abil
ity
ofea
ch e
ven
t fi
rst.
P(r
ed)
��1 38 8�
or � 19 9�
P(b
lack
) �
�1 38 8�or
� 19 9�
Th
en m
ult
iply
.
P(r
ed,t
hen
bla
ck)
�� 19 9�
�� 19 9�
or � 38 61 1�
Fin
d e
ach
pro
bab
ilit
y.
1.bl
ack,
then
bla
ck
� 38 61 1�
2.pr
ime
nu
mbe
r,th
en a
com
posi
te n
um
ber
�1 73 25 2�
3.a
nu
mbe
r co
nta
inin
g at
lea
st o
ne
0,th
en a
nu
mbe
r co
nta
inin
g at
lea
ston
e 2
� 1,6 45 44�
4.re
d,th
en b
lack
� 38 61 1�
5.th
e n
um
bers
rep
rese
nti
ng
you
r ag
e,m
onth
of
birt
h,a
nd
then
day
of
birt
h
� 54,1 87
2�
03
915
20
32 26 4 10 16 21 33 27 5
1117
2234
2800
612
2335291871312430368
214
1931
25
6SD
AP
3.4,
6S
DA
P3.
5
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Wor
d Pr
oble
m P
ract
ice
Co
mp
ou
nd
Eve
nts
Cha
pter
956
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Copyright © Glencoe\McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-8
1.SA
FETY
Eig
hty
per
cen
t of
all
Cal
ifor
nia
driv
ers
wea
r se
at b
elts
.If
thre
e dr
iver
sar
e pu
lled
ove
r,w
hat
is
the
prob
abil
ity
that
all
wou
ld b
e w
eari
ng
thei
r se
atbe
lts?
Wri
te a
s a
perc
ent
to t
he
nea
rest
ten
th.
51.2
%
2.V
EGET
AB
LES
A n
atio
nw
ide
surv
eysh
owed
th
at 6
5% o
f al
l ch
ildr
en i
n t
he
Un
ited
Sta
tes
disl
ike
eati
ng
vege
tabl
es.
If t
hre
e ch
ildr
en a
re c
hos
en a
t ra
ndo
m,
wh
at i
s th
e pr
obab
ilit
y th
at a
ll t
hre
edi
slik
e ea
tin
g ve
geta
bles
? W
rite
as
ape
rcen
t to
th
e n
eare
st t
enth
.27
.5%
3.Q
UA
LITY
In a
sh
ipm
ent
of 5
0ca
lcu
lato
rs,4
are
def
ecti
ve.O
ne
calc
ula
tor
is r
ando
mly
sel
ecte
d an
dte
sted
.Wh
at i
s th
e pr
obab
ilit
y th
at i
t is
defe
ctiv
e?
� 22 5�
4.M
AR
BLE
SA
bag
con
tain
s 6
gree
nm
arbl
es,2
blu
e m
arbl
es,a
nd
3 w
hit
em
arbl
es.G
wen
dra
ws
one
mar
ble
from
the
jar
and
repl
aces
it.
Jeff
th
en d
raw
son
e m
arbl
e fr
om t
he
jar.
Wh
at i
s th
epr
obab
ilit
y th
at G
wen
dra
ws
a bl
ue
mar
ble
and
Jeff
dra
ws
a w
hit
e m
arbl
e?� 16 21�
5.D
EMO
NST
RA
TIO
NM
s.M
orri
s n
eeds
ast
ude
nt
to h
elp
her
wit
h a
dem
onst
rati
on f
or h
er c
lass
of
12 g
irls
and
14 b
oys.
Sh
e ra
ndo
mly
ch
oose
s a
stu
den
t.W
hat
is
the
prob
abil
ity
that
she
choo
ses
a gi
rl?
� 16 3�
6.SU
RV
EYR
ube
n s
urv
eyed
his
cla
ss a
nd
fou
nd
that
4 o
ut
of 2
2 st
ude
nts
wal
k to
sch
ool.
If o
ne
of t
he
22 s
tude
nts
is
sele
cted
at
ran
dom
,wh
at i
s th
epr
obab
ilit
y th
at t
he
chos
en s
tude
nt
DO
ES
NO
T w
alk
to s
choo
l?
� 19 1�
6SD
AP
3.4,
6S
DA
P3.
5
Answers (Lesson 9-8)
Chapter 9 A25 Glencoe California Mathematics, Grade 6
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
TI-7
3 A
ctiv
ityP
rob
abili
ty a
nd
Per
cen
ts
Cha
pter
958
Gle
ncoe
Cal
iforn
ia M
athe
mat
ics,
Gra
de 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9-8
Whe
n yo
u so
lve
prob
abili
ty p
robl
ems,
use
your
cal
cula
tor
to e
xpre
ss f
ract
ions
as
deci
mal
san
d pe
rcen
ts.
Tw
o nu
mbe
r cu
bes
are
rolle
d.F
ind
the
prob
abili
ty t
hat
both
cub
es s
how
an
odd
num
ber.
Rep
ort
the
prob
abili
ty a
s a
perc
ent.
The
pro
babi
lity
of
a cu
be s
how
ing
an o
dd n
umbe
r is
�1 2� . T
o fi
nd th
e pr
obab
ilit
yth
at b
oth
firs
t and
sec
ond
cube
s ar
e od
d, m
ulti
ply
�1 2�by
�1 2� .
Key
s: 1
2
1 2
Dis
play
: � 21 �
* � 21 �
� 41 �
� 41 �.25
100
Ans
*100
25
The
pro
babi
lity
that
bot
h cu
bes
show
odd
num
bers
is 2
5%.
The
re a
re 3
red
mar
bles
and
5 b
lue
mar
bles
in a
bag
.Tw
o m
arbl
es a
re d
raw
nan
d th
e fi
rst m
arbl
e is
rep
lace
d be
fore
the
seco
nd is
dra
wn.
Wha
t is
the
prob
abili
ty o
f dra
win
g 2
blue
mar
bles
? R
epor
t the
pro
babi
lity
as a
per
cent
.
Key
s:
Dis
play
:
5 8
5 8
� 85 � *� 85 �
� 625 4�
Dis
play
:�625 4�
0.390
625
100
Dis
play
:Ans
*100
0.390
625
The
pro
babi
lity
of
draw
ing
2 bl
ue m
arbl
es is
39.
06%
.
Fin
d e
ach
pro
bab
ilit
y.R
epor
t yo
ur
answ
er a
s a
per
cen
t.R
oun
d p
erce
nts
to
the
nea
rest
hu
nd
red
th w
hen
nec
essa
ry.
1.Y
ou d
raw
2 m
arbl
es f
rom
a b
ag r
epla
cing
the
firs
t mar
ble
befo
re d
raw
ing
the
seco
nd. T
he b
agco
ntai
ns 4
yel
low
mar
bles
, 2 w
hite
mar
bles
, and
6 r
ed m
arbl
es.
a.W
hat i
s th
e pr
obab
ilit
y th
at y
our
firs
t mar
ble
is r
ed a
nd th
e se
cond
is y
ello
w?
16.6
7%b.
Wha
t is
the
prob
abil
ity
that
bot
h m
arbl
es a
re w
hite
?2.
78%
c.W
hat i
s th
e pr
obab
ilit
y th
at n
eith
er m
arbl
e is
red
?25
%d.
Wha
t is
the
prob
abil
ity
that
bot
h m
arbl
es a
re r
ed?
25%
2.Y
ou h
ave
thre
e nu
mbe
r cu
bes.
a.W
hat i
s th
e pr
obab
ilit
y th
at y
ou w
ill r
oll a
ll e
ven
num
bers
?12
.5%
b.W
hat i
s th
e pr
obab
ilit
y th
at y
ou w
ill r
oll o
nly
num
bers
less
than
3?
3.70
%c.
CH
ALL
ENG
EW
hat i
s th
e pr
obab
ilit
y th
at y
ou w
ill r
oll a
1 o
n on
ly o
ne n
umbe
r cu
be?
27.7
8%
EN
TE
R
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Exam
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Answers (Lesson 9-8)
Chapter 9 A26 Glencoe California Mathematics, Grade 6
Chapter 9 A27 Glencoe California Mathematics, Grade 6
An
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c.Chapter 9 Assessment Answer Key
Quiz 1 (Lessons 9-1 and 9-2) Quiz 3 (Lessons 9-5 and 9-6) Mid-Chapter TestPage 61 Page 62 Page 63
Quiz 2 (Lessons 9-3 and 9-4)
Page 61Quiz 4 (Lessons 9-7 and 9-8)
Page 62
1.
2.
3.
4.
5. C
See students’ work.There are 24
arrangements.
�1136�
�12
�
�12
�
1.
2.
3.
4.
5. 40,320
120
756
824
1.
2.
3.
4.
5. 30
6
84
210
126
1.
2.
3.
4.
5.�210�
�152�
�16�; Sample answer:
The theoreticalprobability is less
than the experimentalprobability.
�25
�
�13
�
7.
8.
9.
10.
11.
12.
13. 140
9
8
120
30
64
1.
2.
3.
4.
5.
6. J
B
F
B
G
B
Chapter 9 Assessment Answer KeyVocabulary Test Form 1Page 64 Page 65 Page 66
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Sample answer: If eventM can occur in m waysand is followed by eventN that can occur in nways, then event Mfollowed by N can occurin m � n ways.
compound event
fair game
combination
probability
permutation
complementary event
sample space
independent event
experimentalprobability
outcome 1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12. H
C
G
D
J
C
H
A
G
A
G
D 13.
14.
15.
16.
17.
18.
19.
20. F
D
F
B
F
C
J
C
B:�315�
Chapter 9 A28 Glencoe California Mathematics, Grade 6
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Chapter 9 A29 Glencoe California Mathematics, Grade 6
An
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Form 2A Form 2BPage 67 Page 68 Page 69 Page 70
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12. H
D
G
A
F
B
J
B
H
A
G
D 13.
14.
15.
16.
17.
18.
19.
20. G
C
H
C
H
B
J
A
B:�210�
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11. A
J
B
F
C
J
B
H
C
H
D
B:�115�
12.
13.
14.
15.
16.
17.
18.
19.
20. G
B
G
B
F
B
J
B
J
Chapter 9 A30 Glencoe California Mathematics, Grade 6
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Form 2CPage 71 Page 72
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11. permutation; 720
combination; 126
combination; 15
permutation; 210
144
240
1,512
�14
�
�12
�
See students’ work.There are 12 possible
ornaments.
See students’ work.There are
24 possibilities.12.
13.
14.
15.
16.
17.
18.
19.
20.
B: 3,276,000
�1415�
�2156�
�314�
It is less than theexperimentalprobability.
�59
�
�47
�
�37
�
91
136,080
Chapter 9 A31 Glencoe California Mathematics, Grade 6
An
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s
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Form 2DPage 73 Page 74
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11. combination; 35
permutation; 120
permutation; 56
combination; 120
18
12
450
�14
�
�12
�
See students’ work.There are 6
possible orders.
See students’ work.There are 24
arrangements. 12.
13.
14.
15.
16.
17.
18.
19.
20.
B: 468,000
�121�
�112�
�114�
It is less than theexperimentalprobability.
�13
�
�25
�
�35
�
165
544,320
Chapter 9 A32 Glencoe California Mathematics, Grade 6
Copyright ©
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raw-H
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Form 3Page 75 Page 76
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
permutation;15,600
combination; 35
combination; 70
permutation; 720
24
480
441
�58
�
�12
�
See students’ work.There are 8 possible
song types.
See students’ work.There are 6 possible
arrangements.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B: 7,862,400
�5,5
125�
�1114�
�245�
It is less than theexperimentalprobability.
�38
�
�35
�
�35
�
220
3,276,000
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Chapter 9 A33 Glencoe California Mathematics, Grade 6
An
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Chapter 9 Assessment Answer Key Page 77, Extended-Response Test
Scoring Rubric
Level Specific Criteria
4 The student demonstrates a thorough understanding of the mathematicsconcepts and/or procedures embodied in the task. The student hasresponded correctly to the task, used mathematically sound procedures,and provided clear and complete explanations and interpretations. Theresponse may contain minor flaws that do not detract from thedemonstration of a thorough understanding.
3 The student demonstrates an understanding of the mathematics conceptsand/or procedures embodied in the task. The student’s response to thetask is essentially correct with the mathematical procedures used and theexplanations and interpretations provided demonstrating an essential butless than thorough understanding. The response may contain minor errorsthat reflect inattentive execution of the mathematical procedures orindications of some misunderstanding of the underlying mathematicsconcepts and/or procedures.
2 The student has demonstrated only a partial understanding of themathematics concepts and/or procedures embodied in the task. Althoughthe student may have used the correct approach to obtaining a solution ormay have provided a correct solution, the student’s work lacks an essentialunderstanding of the underlying mathematical concepts. The responsecontains errors related to misunderstanding important aspects of the task,misuse of mathematical procedures, or faulty interpretations of results.
1 The student has demonstrated a very limited understanding of themathematics concepts and/or procedures embodied in the task. Thestudent’s response to the task is incomplete and exhibits many flaws.Although the student has addressed some of the conditions of the task, thestudent reached an inadequate conclusion and/or provided reasoning thatwas faulty or incomplete. The response exhibits many errors or may beincomplete.
0 The student has provided a completely incorrect solution oruninterpretable response, or no response at all.
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Chapter 9 A34 Glencoe California Mathematics, Grade 6
Chapter 9 Assessment Answer Key Page 77, Extended-Response Test
Sample Answers
1. a. There are 4 possible outcomeshaving an equal chance of occurring.
number of ways to spin a 1
number of possible outcomes
b. Spin spinner B 100 times and tallythe number of times you spin W.
P(W) � �1n00�
number of times you spin W
2. a.
b. If the outcome of one event does notinfluence the outcome of a secondevent, the events are calledindependent events.
c. To find the probability of tossing ahead and drawing a red marble,write the number of ways to toss ahead and draw a red marble (2) overthe number of possible outcomes.P(H, R) � P(H) · P(R) � �
12� · �
26� � �
16�,
since they are independent events.
d. P(B, then B) � P(B) · P(B after B)
� �12� · �
25� � �
15�
The probability of the first event is �12�
because �12� of the marbles are blue.
The probability of the second event
is �25� because the blue marble drawn
was not replaced. Two of theremaining five marbles are blue.
3. a. Each time Rayna chooses one of eachtype of relative is an event. Theevent of choosing a niece can occurin 8 ways, choosing a nephew canoccur in 9 ways, and so on. So, Raynacould choose a possible 8 � 9 � 6 � 3 � 5 � 6,480 teams.
b. 8 � 7 � 6 � 5 � 4 � 3 � 2 � 1 � 40,320;The order of the arrangement of the nieces is important, so apermutation, is used.
c.
� 44,352,165
The order of their arrangement isnot important, so a combination isused.
31 � 30 � 29 � 28 �27 � 26 � 25 � 24 � 23 � 22����10 � 9 � 8 � 7 � 6 � 5 �
4 � 3 � 2 � 1
H
MarbleDraw
CoinToss
SampleSpace
W HWHB1HB2HB3HR1HR2
B3
B2
B1
R1R2
T
W TWTB1TB2TB3TR1TR2
B3
B2
B1
R1R2
→
→
→
P(1) � �14�
In addition to the scoring rubric found on page A33, the following sample answersmay be used as guidance in evaluating extended-response assessment items.
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Chapter 9 A35 Glencoe California Mathematics, Grade 6
An
swer
s
Chapter 9 Assessment Answer KeyStandardized Test PracticePage 78 Page 79
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12. F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D 13.
14.
15.
16.
17.
18.
19. A B C D
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
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Chapter 9 A36 Glencoe California Mathematics, Grade 6
Chapter 9 Assessment Answer KeyStandardized Test PracticePage 80
20.
21.
22.
23.
24.
25a.
25b.
There are 8 people,so the number ofarrangements is 8! � 40,320.
Order is important,so this is apermutation. Thereare 3 women, 3 men,and 2 children so the number of waysto arrange them is(3!)(3!)(2!) � 72.
1,716
13%
1�38
�
�245�
20
Chapter 9 A37 Glencoe California Mathematics, Grade 6
An
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Unit 4 Test
Page 81 Page 82
1.
2.
3.
4.
5.
6.
7.
8.
Sample answer: Thevertical axis does not startat zero. Therefore, itexaggerates the number oftelevisions for the USA. Itlooks double that of Japan.
15
$8; $7; $5
Sample answer:110 mm
Sample answer:Cluster 69–76; gaps
65–69, 76–78; nooutliers
72 mph
169.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.independent; �2
100�
permutation;39, 916, 800
combination;3,003
1,360
See students’ treediagrams; 18outcomes
�23
�
�16
�
�12
�
�13
�
�16
�
�1531�
�14
�
Stem Leaf2 5 93 5 84 0 3 5 7 5 0 6
3|2 � 32