Chapter 3 Review ESSAY. Write your answer in the space ...

[Pages:7]Chapter 3 Review ESSAY. Write your answer in the space provided or on a separate sheet of paper.

Solve the problem. 1) A bag of colored candies contains 20 red, 25 yellow, and 35 orange candies. An experiment consists of randomly choosing one candy from the bag and recording its color. What is the sample space for this experiment?

2) An experiment consists of randomly choosing a number between 1 and 10. Let E be the event that the number chosen is even. List the sample points in E.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

3) Fill in the blank. The __________ of two events A and B is the event that either A or B or both

3)

occur.

A) union

B) Venn diagram

C) intersection

D) complement

4) Fill in the blank. The __________ of two events A and B is the event that both A and B occur.

4)

A) complement

B) Venn diagram

C) intersection

D) union

5) A state energy agency mailed questionnaires on energy conservation to 1,000 homeowners in the 5) state capital. Five hundred questionnaires were returned. Suppose an experiment consists of randomly selecting one of the returned questionnaires. Consider the events:

A: {The home is constructed of brick} B: {The home is more than 30 years old}

In terms of A and B, describe a home that is constructed of brick and is less than or equal to 30

years old.

A) A B

B) A Bc

C) (A B)c

D) A B

6) An insurance company looks at many factors when determining how much insurance will cost for 6) a home. Two of the factors are listed below:

A: {The home's roof is less than 10 years old} B: {The home has a security system}

In the words of the problem, define the event Bc. A) The home is not less than 10 years old B) The home does not have a security system C) The home is less than 10 years old D) The home has a security system

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7) A state energy agency mailed questionnaires on energy conservation to 1,000 homeowners in the 7) state capital. Five hundred questionnaires were returned. Suppose an experiment consists of randomly selecting one of the returned questionnaires. Consider the events:

A: {The home is constructed of brick} B: {The home is more than 30 years old} D: {The home is heated with oil}

Which of the following describes the event B Dc? A) homes more than 30 years old that are not heated with oil B) homes more than 30 years old that are heated with oil C) homes more than 30 years old or homes that are not heated with oil D) homes that are not older than 30 years old and heated with oil

SHORT ANSWER.

8) Probabilities of different types of vehicle-to-vehicle accidents are shown below:

8)

Accident Probability

Car to Car

0.66

Car to Truck 0.18

Truck to Truck 0.16

Find the probability that an accident involves a car.

9) At a small private college with 800 students, 240 students receive some form of

9)

government-sponsored financial aid. Find the probability that a randomly selected

student receives some form of government-sponsored financial aid.

10) The table displays the probabilities for each of the six outcomes when rolling a particular 10) unfair die. Find the probability that the number rolled on a single roll of this die is less than 4.

Outcome

1

2

3

4

5

6

Probability

.1

.1

.1

.2

.2

.3

11) The table shows the number of each type of book found at an online auction site during a 11) recent search. Suppose that Juanita randomly chose one book to bid on and then noted its type.

Type of Book Children's Fiction Nonfiction Educational

Number 51,033 141,114 253,074 67,252

a. List the sample points for this experiment. b. Find the probability of each sample point. c. What is the probability that the book was nonfiction or educational?

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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

12) A clothing vendor estimates that 78 out of every 100 of its online customers do not live within 50

12)

miles of one of its physical stores. Using this estimate, what is that probability that a a randomly

selected online customer lives within 50 miles of a physical store?

A) .50

B) .28

C) .22

D) .78

SHORT ANSWER.

13) The following data represent the scores of 50 students on a statistics exam. Suppose that

13)

one of the 50 students is chosen at random and that student's score is noted.

39 51 59 63 66 68 68 69 70 71 71 71 73 74 76 76 76 77 78 79 79 79 79 80 80 82 83 83 83 85 85 86 86 88 88 88 88 89 89 89 90 90 91 91 92 95 96 97 97 98

a. What is the probability that the student's score is 88? b. What is the probability that the student's score is less than 60? c. What is the probability that the student's score is between 70 and 79, inclusive?

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 14) A number between 1 and 10, inclusive, is randomly chosen. Events A and B are defined as follows. 14)

A: {The number is even} B: {The number is less than 7}

Identify the sample points in the event A B. A) {1, 2, 3, 4, 5, 6, 7, 9} C) {1, 2, 3, 4, 5, 6, 8, 10}

B) {2, 4, 6} D) {1, 2, 3, 4, 5, 6, 7, 8, 10}

15) A number between 1 and 10, inclusive, is randomly chosen. Events A and B are defined as follows. 15)

A: {The number is even} B: {The number is less than 7}

Identify the sample points in the event A B. A) {1, 2, 3, 4, 5, 6, 7, 9} C) {2, 4, 6}

B) {1, 2, 3, 4, 5, 6, 7, 8, 10} D) {1, 2, 3, 4, 5, 6, 8, 10}

16) A pair of fair dice is tossed. Events A and B are defined as follows.

16)

A: {The sum of the numbers on the dice is 3} B: {At least one of the dice shows a 2}

Identify the sample points in the event A B. A) {(1, 2), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)} B) {(2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (4, 2), (5, 2), (6, 2)} C) {(1, 2), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (4, 2), (5, 2), (6, 2)} D) {(1, 2), (2, 1)}

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17) Each manager of a corporation was rated as being either a good, fair, or poor manager by his/her 17) boss. The manager's educational background was also noted. The data appear below:

Educational Background

Manager

Rating H. S. Degree Some College College Degree Master's or Ph.D. Totals

Good

2

8

24

5

39

Fair

3

15

49

20

87

Poor

1

9

6

18

34

Totals

6

32

79

43

160

If we randomly selected one manager from this company, find the probability that he or she has

an advanced (Master's or Ph.D.) degree and is a good manager.

A)

41 80

B)

29 40

C)

1 32

D)

31 32

18) Four hundred accidents that occurred on a Saturday night were analyzed. The number of vehicles 18) involved and whether alcohol played a role in the accident were recorded. The results are shown below:

Number of Vehicles Involved

Did Alcohol Play a Role? 1

2 3 or more Totals

Yes

59 98

13

170

No

20 171

39

230

Totals

79 269

52

400

Suppose that one of the 400 accidents is chosen at random. What is the probability that the

accident involved more than a single vehicle?

A)

79 400

B)

13 400

C)

13 100

D)

321 400

19) A sample of 350 students was selected and each was asked the make of their automobile (foreign 19) or domestic) and their year in college (freshman, sophomore, junior, or senior). The results are shown in the table below.

What is the probability of randomly selecting a student who is in the freshman class or drives a

foreign automobile?

A) 230/350

B) 15/350

C) 15/205

D) 215/350

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SHORT ANSWER.

20) The table shows the number of each Ford car sold in the United States in June. Suppose

20)

the sales record for one of these cars is randomly selected and the type of car is identified.

Type of Car Sedan Convertible Wagon SUV Van Hatchback Total

Number 7,204 9,089 20,418 13,691 15,837 15,350 81,589

Events A and B are defined as follows.

A: {Convertible, SUV, Van} B: {Fewer than 10,000 of the type of car were sold in June}

a. Identify the sample points in the event A B. b. Identify the sample points in the event A B. c. Find P(A B). d. Find P(A B).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

21)

For

two

events,

A

and

B, P(A)

=

1 2

,

P(B)

=

1, 3

and

P(A

B)

=

1. 4

Find

P(B

|

A).

21)

A)

3 4

B)

1 2

C)

1 12

D)

1 8

22) A sample of 350 students was selected and each was asked the make of their automobile (foreign 22) or domestic) and their year in college (freshman, sophomore, junior, or senior). The results are shown in the table below.

Given that you know the selected student is in the senior class, find the probability they drive a

domestic automobile.

A) 15/205

B) 10/35

C) 15/350

D) 25/35

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23) The manager of a used car lot took inventory of the automobiles on his lot and constructed the

23)

following table based on the age of each car and its make (foreign or domestic):

Make Foreign Domestic Total

0 - 2 43 36 79

Age of Car (in years)

3 - 5 6 - 10

26

10

28

14

54

24

over 10 21 22 43

Total 100 100 200

A car was randomly selected from the lot. Given that the car selected was a foreign car, what is the

probability that it was older than 2 years old?

A)

43 121

B)

57 100

C)

43 100

D)

57 121

24) A local country club has a membership of 600 and operates facilities that include an 18-hole

24)

championship golf course and 12 tennis courts. Before deciding whether to accept new members,

the club president would like to know how many members regularly use each facility. A survey of

the membership indicates that 57% regularly use the golf course, 48% regularly use the tennis

courts, and 9% use both of these facilities regularly. Given that a randomly selected member uses

the tennis courts regularly, find the probability that they also use the golf course regularly.

A) .1343

B) .7164

C) .1875

D) .4737

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Answer Key Testname: CH3 REVIEW

1) {red, yellow, orange}

2) {2, 4, 6, 8, 10}

3) A

4) C

5) B

6) B

7) C

8) 0.84

9)

P(receives government aid) =

240 800

= .3

10) .3

11) a. {children's, fiction, nonfiction, educational}

b.

Type of Book

Probability

Children's

.10

Fiction

.28

Nonfiction

.49

Educational

.13

c. 12) C

13) a.

P(nonfiction) + P(educational) = .49 + .13 = .62

P(88)

=

4 50

=

2 25

b.

P(less than 60) =

3 50

c.

P(between

70

and

79,

inclusive)

=

15 50

=

3 10

14) C 15) C 16) C 17) C 18) D 19) D 20) a.

b.

c.

{Sedan, Convertible, SUV, Van}

{Convertible}

P(A

B)

=

7,204

+

9,089 + 13,691 81,589

+

15,387

=

45,821 81,589

.56

d.

P(A B) =

9.089 81,589

.11

21) B 22) B 23) B 24) C

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