Math 10 Name KcU Exam 4: Chapter 12 3 " Each problem is worth 10 points. You must show all work to receive full credit.

1. Match the word with the definition.

Deflnitions Words

i . An \ is a controlled operation that yields a set of results. a. event

i i . The possible resuhs of an experiment are called its \ b. sample point

ii i . An i^'^ is a subcoUection of the outcomes of an experiment. c. permutation

iv. is the relative frequency of occurrence of an event and is d. mutually

detei mined by actual observations of an experiment. exclusive

V. I is detei mined through a study of the possible outcomes that can e. conditional

occur for the given experiment. probability

vi. If each outcome of an experiment has the same chance of occurring as f independent

any other outcome, they are said to be \ events

vii. A list of all possible outcomes of an experiment is called a \ g- combination

viii. V \e illustrated flow charts used to determine sample spaces. h. tree diagrams

ix. Two events A and B are (\f it is impossible for both events to occur i. theoretical

simultaneously. probability

X. Event A and event B are ^ if the occurrence of either event in no J- sample space

way affects the probability of occurrence of the other event.

xi. The probability of event Ej occurring, given that an event E\s k. equally likely

happened (or will happen; the time relationship does not matter), is outcomes

called a \d is written P(ii2|£'i).

xii. A ( is any ordered arrangement of a given set of objects. 1. experiment

xiii . A ' ^ is a distinct group (or set) of objects without regard to their m. empirical

arrangement. probability

n. outcomes

2, If P(A)=0,1, P(B)=0.4, and P(A or B)=035, then find P(A and B).

Two fair dice are rolled. Find the probability of each of the following:

a. P(the sum of the two numbers is 5).

b. P(the sum of the two numbers is even).

c. P(the sum of the two numbers is less than 5).

) (2^JK<4) (2 ,5 ) (2 ,6 ) ,2) (^3) (3,4) (3,5) (3,6)

1>(4,2) (4,3) (4,4) (4,5) (4,6|^ ((5,;) (5,2) (5,3) (5,4) (5,5) (5^j (6,1) (6^) (6,3) (6,4) (6,5) (6^j)

d. P(the sum of the two numbers is even A N D less than 5). - ^ ( j l ' ^ / t N ^

e. P(the sum ofthe two numbers is even OR less than 5). ' ^

5C d<b ONE card is drawn at random from a standard 52-card deck. Find the probability of each of the following: a. P(the card is a king). — M _ \

5 l ' b. P(the card is not a king). _ J

c. P(the card is a number less than 5).

d. P(the card is a number less than 5 OR *).

57. 52-e. P(the card is greater than 3 and less than 6 A N D *).

A fair coin is tossed 3 times. The sample space is hsted below, a. Find P(coin landing on exactly two heads). A

b. Find P(coin landing on no heads).

c. Find P(coin landing on at least one heads)\

d. Find P(coin landing on exactly two heads / T' was heads).

e. Find P(coin landing on no heads /1^' was tails).

Sample Space

II HHH

HHT HTH

HTT THH

THT TTH

TTT

6. A restaurant's lunch specials include soup or salad, chicken or fish, and water or tea or soda, a. How many ways can you have lunch?

appetizer meal beverage total numberof ways

b. Draw a tree diagram and list the sample space.

Sample Space

c. Find P(having fish / that you had a salad).

3 ̂ rn

d. Find P(having soup and tea).

e. Find P(not having chicken nor soda).

1 3

7. Two marbles are drawn from a box with 3 white, 2 green, 2 red, and 1 blue marble. a. Find P(both marbles are white), if the marbles were drawn one at a time with replacement.

b. Find P(both marbles are white), if the marbles were drawn one at a time without replacement.

& ^ ^ ^ ^ c. Find P(one marble is white and one marble is blue), if the marbles were drawn one at a time with

replacement.

16 fc d. Find P ( l ' ' marble is white and 2""̂ marble is blue), i f the marbles were drawn one at a time without

replacement.

e. Say the marbles were drawn at the same time. Find P(one marble is white and one marble is blue, regardless of order), if the marbles were drawn at the same time without replacement.

8. A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at random. a. Find P(all 3 candies are cherry), i f the candies were drawn at the same time without replacement.

b. Find P(no cherry candies), i f the candies were drawn at the same time without replacement.

c. Find P(at least 1 cherry candy), i f the candies were drawn at the same time without replacement.

' Pipe cbm) 35 ' \'o

d. Find P(exactly 2 cherry candies and any other candy, in any order), i f the candies were drawn at the same time without replacement. , \: |

e. Say the candies were drawn one at a time. Find P(r' is cherry, 2"*̂ is orange, and 3''̂ is lemon), i f they were drawn without replacement.

9. A license plate is to consist of 2 letters followed by 3 digits. Determine the number of different license plates possible i f a. Repetition of letters and number^s permitted.

- N L L # « # ^

b. Repetition of letters and numbers is NOT permitted.

L L # # #

c. The r' letter has to be a vowel (a, e, i, o, u) and the l " number has to be less than 4. Also, repetition of letters and numbers is permitted.

L L # # ft

d. The 1̂ ' letter has to be a vowel (a, e, i, o, u) and the 1̂ ' number has to be less than 4. Also, repetition of letters and numbers is NOT permitted.

L L U # U '

10. Calculate

11. Calculate a. X „

12. You want to arrange 5 books (math, science, history, biology, and English) on a bookshelf a. How many different ways can all 5 books be arranged?

b. How many different ways can the 5 books be arranged i f math is in the middle?

iL 1 .1. ̂ - L =|l4_\ c. How many different ways can the 5 books be arranged if math is in the middle and history is on the

end? V

:^ ^ A_ 1- =\(^ d. How many different ways can the 5 books be arranged i f science is first, math is in the middle and

history is on the end?

e. How many different ways can the books be arranged if you threw out 2 books and only kept 3 of the

13. How many ways can you arrange the word COMMUNICATION?

14. Say there were 7 women and 5 men applying for 7 positions at a company. a. Find the number of different combinations the company can hire the 7 people.

b. Find the number of different combinations the company can hire the 7 people, i f 4 have to women and 3 have to be men.

15. A pool table has balls numbered 1-15, where 7 are striped and 8 are solid. You randomly shot in 5 balls all at the same time. Use combinations to calculate the following: a. P(you shot in all 5 solids). ^ \

b. P(you shot in all 5 stripes).

c. P(you shot in all 5 balls numbered greater than^).

d. P(you shot in 3 stripes and 2 solids at the same time).

e. P(you shot in 3 stripes, and then 2 solids).