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A) 0.56 B) 0.01 C) 0.006 D) 0.005
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# Question : A) 0.56 B) 0.01 C) 0.006 D) 0.005 : 2151664

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

Solve the problem.

1) 45% of a store's computers come from factory A and the remainder come from factory B. 4% of computers from factory A are defective while 1% of computers from factory B are defective. If one of the store's computers is selected at random, what is the probability that it is defective and from factory B?

A) 0.56

B) 0.01

C) 0.006

D) 0.005

2) 36% of a store's computers come from factory A and the remainder come from factory B. 4% of computers from factory A are defective while 3% of computers from factory B are defective. If one of the store's computers is selected at random, what is the probability that it is not defective and from factory A?

A) 0.966

B) 0.346

C) 0.96

D) 0.014

3) In a certain U.S. city, 51.5% of adults are women. In that city, 12.3% of women and 10.5% of men suffer from depression. If an adult is selected at random from the city, find the probability that the person is a man who does not suffer from depression.

A) 0.895

B) 0.461

C) 0.051

D) 0.434

4) In a certain U.S. city, 51.4% of adults are women. In that city, 14.2% of women and 10.2% of men suffer from depression. If an adult is selected at random from the city, find the probability that the person suffers from depression.

A) 0.142

B) 0.123

C) 0.122

D) 0.073

5) Steve lives in Tewin Wood, a wooded area prone to power outages during storms due to falling trees.

The probability that there will be a storm tomorrow in Tewin Wood is 0.11. If there is a storm, the probability that there will be a power outage is 0.10. If there is no storm, there will not be a power outage.

What is the probability that Steve will not have a power outage tomorrow?

A) 0.89

B) 0.8010

C) 0.9890

D) 0.0990

6) The probability that a person passes a test on the first try is 0.69. The probability that a person who fails the first test will pass on the second try is 0.76. The probability that a person who fails the first and second tests will pass the third time is 0.61. Find the probability that a person fails the first and second tests and passes on the third try.

A) 0.3199

B) 0.0290

C) 0.61

D) 0.0454

7) The probability that a person passes a test on the first try is 0.65. The probability that a person who fails the first test will pass on the second try is 0.75. The probability that a person who fails the first and second tests will pass the third time is 0.62. Find the probability that a person who is prepared to take the test a maximum of three times will pass.

A) 0.9125

B) 0.3023

C) 0.9668

D) 0.0543

8) Two stores sell a certain product. Store A has 38% of the sales, 4% of which are of defective items, and store B has 62% of the sales, 5% of which are of defective items. The difference in defective rates is due to different levels of pre-sale checking of the product. A person receives one of this product as a gift. What is the probability it is defective?

A) 0.045

B) 0.023

C) 0.42

D) 0.046

9) A company is conducting a sweepstakes, and ships two boxes of game pieces to a particular store. Box A has 2% of its contents being winners, while 4% of the contents of box B are winners. Box A contains 25% of the total tickets. If the contents of both boxes are mixed in a drawer and a ticket is chosen at random, what is the probability it is a winner?

A) 0.06

B) 0.005

C) 0.03

D) 0.035

10) A teacher designs a test so a student who studies will pass 90% of the time, but a student who does not study will pass 11% of the time. A certain student studies for 85% of the tests taken. On a given test, what is the probability that student passes?

A) 0.505

B) 0.765

C) 0.165

D) 0.782

Use the given table to find the indicated probability.

11) College students were given three choices of pizza toppings and asked to choose one favorite. The following table shows the results.

A student is selected at random. Find the probability that the student's favorite topping is meat given that the student is a junior.

A) 0.061

B) 0.188

C) 0.296

D) 0.207

12) College students were given three choices of pizza toppings and asked to choose one favorite. The following table shows the results.

A student is selected at random. Find the probability that the student's favorite topping is veggie given that the student is a junior or senior.

A) 0.392

B) 0.219

C) 0.379

D) 0.662

13) People in a survey were given three choices of soft drinks and asked to choose one favorite. The following table shows the results.

One of the participants is selected at random. Find the probability that the person is over 40 and prefers cola.

A) (4/51)

B) (4/17)

C) (4/19)

D) none of the above

14) People in a survey were given three choices of soft drinks and asked to choose one favorite. The following table shows the results.

One of the participants is selected at random. Find the probability that the person is over 40 given that they prefer root beer.

A) (6/17)

B) (2/5)

C) (2/17)

D) (5/17)

15) People in a survey were given three choices of soft drinks and asked to choose one favorite. The following table shows the results.

One of the participants is selected at random. Find the probability that the person prefers root beer given that they are over 40.

A) (2/5)

B) (6/17)

C) (2/17)

D) (20/51)

16) The following table contains data from a study of two airlines which fly to Smalltown, USA.

If a flight is selected at random, what is the probability that it was on time given that it was on Upstate Airlines?

A) (43/76)

B) (43/48)

C) (11/76)

D) (43/87)

17) The following table contains data from a study of two airlines which fly to Smalltown, USA.

If a flight is selected at random, what is the probability that it was on Upstate Airlines given that it arrived late?

A) (5/11)

B) (5/48)

C) (54/87)

D) (5/87)

18) The following table contains data from a study of two airlines which fly to Smalltown, USA.

If a flight is selected at random, what is the probability that it was on Upstate Airlines and that it arrived on time?

A) (43/48)

B) (11/76)

C) (43/76)

D) (43/87)

Find the indicated probability.

19) The following contingency table provides a joint frequency distribution for the popular votes cast in the 1984 presidential election by region and political party. Data are in thousands, rounded to the nearest thousand.

Political Party

A person who voted in the 1984 presidential election is selected at random. Compute the probability that the person selected voted Democrat.

A) 0.241

B) 0.406

C) 0.098

D) 0.442

20) The following contingency table provides a joint frequency distribution for the popular votes cast in the 1984 presidential election by region and political party. Data are in thousands, rounded to the nearest thousand.

Political Party

A person who voted in the 1984 presidential election is selected at random. Compute the probability that the person selected did not vote Republican given that they are from the West.

A) 0.404

B) 0.596

C) 0.885

D) 0.078

21) The following contingency table provides a joint frequency distribution for the popular votes cast in the 1984 presidential election by region and political party. Data are in thousands, rounded to the nearest thousand.

Political Party

A person who voted in the 1984 presidential election is selected at random. Compute the probability that the person selected is not from the South given that they voted Democrat.

A) 0.287

B) 0.707

C) 0.293

D) 0.881

22) The following contingency table provides a joint frequency distribution for the popular votes cast in the 1984 presidential election by region and political party. Data are in thousands, rounded to the nearest thousand.

Political Party

A person who voted in the 1984 presidential election is selected at random. Compute the probability that the person selected voted Democrat given that they are from the Midwest.

A) 0.280

B) 0.413

C) 0.113

D) 0.567

23) The following contingency table provides a joint frequency distribution for the popular votes cast in the 1984 presidential election by region and political party. Data are in thousands, rounded to the nearest thousand.

Political Party

A person who voted in the 1984 presidential election is selected at random. Compute the probability that the person selected was in the West and voted Republican.

A) 0.115

B) 0.781

C) 0.588

D) 0.196

24) The following contingency table provides a joint frequency distribution for a group of retired people by career and age at retirement.

Age at Retirement

Suppose one of these people is selected at random. Compute the probability that the person selected was a store clerk.

A) 0.099

B) 0.251

C) 0.025

D) 0.286

25) The following contingency table provides a joint frequency distribution for a group of retired people by career and age at retirement.

Age at Retirement

Suppose one of these people is selected at random. Compute the probability that the person selected was an attorney who retired between 61 and 65.

A) 0.130

B) 0.425

C) 0.255

D) 0.306

26) The following contingency table provides a joint frequency distribution for a group of retired people by career and age at retirement.

Age at Retirement

Suppose one of these people is selected at random. Compute the probability that the person either retired between 56 and 60 or was an administrative assistant.

A) 0.064

B) 0.253

C) 0.409

D) 0.473

27) The table below describes the smoking habits of a group of asthma sufferers.

If one of the 981 subjects is randomly selected, find the probability that the person chosen is a nonsmoker given that it is a woman. Round to the nearest thousandth.

A) 0.556

B) 0.741

C) 0.436

D) 0.398

28) The table below describes the smoking habits of a group of asthma sufferers.

If one of the 942 subjects is randomly selected, find the probability that the person chosen is a woman given that the person is a light smoker.

A) 0.268

B) 0.168

C) 0.519

D) 0.087

Find the probability.

29) Assuming that boy and girl babies are equally likely, find the probability that a family with three children has all boys given that the first two are boys.

A) (1/2)

B) (1/4)

C) (1/8)

D) 1

30) Assuming that boy and girl babies are equally likely, find the probability that a family with four children has all boys given that the first is a boy.

A) (1/8)

B) (1/16)

C) 0

D) (1/4)

31) Assuming that boy and girl babies are equally likely, find the probability that a family with four children has all boys given that the first two are boys.

A) 1

B) (1/4)

C) (1/8)

D) (1/2)

32) Assuming that boy and girl babies are equally likely, find the probability that a family with four children has all boys given that at least one is a boy.

A) (1/8)

B) (1/16)

C) (1/4)

D) (1/15)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

33) Define mutually exclusive events and independent events. Give an example of each.

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

34) Suppose that S and T are mutually exclusive events. Which of the following statements is true?

A) S and T must also be independent.

B) S and T may or may not be independent.

C) S and T cannot possibly be independent.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

35) A card is selected randomly from a standard deck of 52 cards. Let

A = event that the card is an ace.

Give examples of events B, C, and D such that A and B are independent, A and C are dependent but not mutually exclusive, and A and D are mutually exclusive.

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

36) Which (if any) of the following statements is/are true?

A: If two events are dependent, then they must be mutually exclusive

B: If two events are mutually exclusive, then they must be dependent

A) Both statements are true.

B) A only

C) B only

D) Neither statement is true.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

37) Two cards are selected at random from a standard deck of 52 cards. Let

A = event the first card is a queen

B = event the second card is a queen.

(a) If the first card is replaced before the second one is drawn, are events A and B independent? Which rule could you use to find P(A &B)?

(B) If the first card is not replaced before the second one is drawn, are events A and B independent? Which rule could you use to find P(A &B)?

38) If P(A∩B) = 0.2, P(A) = 0.8, P(B) = 0.6, can A and B be independent events? How can you tell?

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

39) Is P(A?B) always less than or equal to P(A)?

A) No

B) Yes

40) Can P(A?B) = P(B?A) if A and B are different?

A) No

B) Yes

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

41) If P(A) = P(A?B), why must P(B) = P(B?A)?

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

42) If A and B are independent events, how many of the following statements must be true?

(i) A' and B are independent.

(ii) A and B' are independent.

(iii) A' and B' are independent.

A) One

B) All

C) Two

D) None

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