Ch04 – Ch 4 Prep Questions – Fundamental Probability Concepts

Analytical Methods for Business (University of Arizona)

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ch04

*Student:*

1. For an experiment in which a single die is rolled, the sample space may be {1, 1, 2, 3, 4, 5}. True False

2. The probability of a union of events can be greater than 1. True False

3. Events are exhaustive if they do not share common outcomes of a sample space. True False

4. Mutually exclusive events may share common outcomes of a sample space. True False

5. Mutually exclusive and collectively exhaustive events contain all outcomes of a sample space, and they do not share any common outcomes.

True False

6. The union of two events *A* and *B*, denoted by , does not have outcomes from both *A* and *B*. True False

7. The complement of an event *A*, denoted by *AC*, within the sample space *S*, is the event consisting of all outcomes of *A* that are not in *S*.

True False

8. The intersection of two events *A* and *B*, denoted by *A* **∩** *B*, is the event consisting of all outcomes that are in *A* and *B*.

True False

9. Subjective probability is assigned to an event by drawing on logical analysis. True False

10. For two independent events *A* and *B*, the probability of their intersection is zero. True False

11. The total probability rule is useful only when the unconditional probability is expressed in terms of probabilities conditional on two mutually exclusive and exhaustive events.

True False

12. Bayes’ theorem uses the total probability rule to update the prior probability of an event that has not been affected by any new evidence.

True False

13. Bayes’ theorem is used to update prior probabilities based on the arrival of new relevant information. True False

14. Combinations are used when the order in which different objects are arranged matters. True False

15. Permutations are used when the order in which different objects are arranged matters. True False

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16. What is probability?

A. Any value between 0 and 1 is always treated as a probability of an event.

B. A numerical value assigned to an event that measures the number of its occurrences.

C. A value between 0 and 1 assigned to an event that measures the likelihood of its occurrence.

D. A value between 0 and 1 assigned to an event that measures the unlikelihood of its occurrence.

17. For an experiment in which a single die is rolled, the sample space is .

A. {1, 1, 3, 4, 5, 6}

B. {2, 1, 3, 6, 5, 4}

C. {1, 2, 3, 4, 4, 5}

D. All of the above

18. A sample space contains .

A. Outcomes of the relevant events

B. Several outcomes of an experiment

C. All possible outcomes of an experiment

D. One of several outcomes of an experiment

19. What is a simple event?

A. An event that contains all outcomes of a sample space

B. An event that contains several outcomes of a sample space

C. An event that contains only one outcome of a sample space

D. All of the above

20. Which of the following is not an event when considering the sample space of tossing two coins?

A. {HH, HT}

B. {HH, TT, HT}

C. {HH, TT, HTH}

D. {HH, HT, TH, TT}

21. Events are collectively exhaustive if .

A. They include all events

B. They are included in all events

C. They contain all outcomes of an experiment

D. They do not share any common outcomes of an experiment

22. Mutually exclusive events .

A. Contain all possible outcomes

B. May share common outcomes

C. Do not share common outcomes

D. Do not contain all possible outcomes

23. Which of the following are mutually exclusive events of an experiment in which two coins are tossed?

A. {TT, HH} and {TT}

B. {HT, TH} and {TH}

C. {TT, HT} and (HT}

D. (TT, HH} and {TH}

24. In an experiment in which a coin is tossed twice, which of the following represents mutually exclusive and collectively exhaustive events?

A. {TT, HH} and {TT, HT}

B. {HT, TH} and {HH, TH}

C. {TT, HH} and {TH, HT}

D. {TT, HT} and {HT, TH}

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25. Which of the following sets of outcomes described below in I and II represent mutually exclusive events?

I. “Your final course grade is an A”; “Your final course grade is a B.”

II. “Your final course grade is an A”; “Your final course grade is a Pass.” A. Neither I nor II represent mutually exclusive events.

B. Both I and II represent mutually exclusive events. C. Only I represents mutually exclusive events.

D. Only II represents mutually exclusive events.

26. Mutually exclusive and collectively exhaustive events .

A. Contain all outcomes in a sample space and may share common outcomes

B. Contain all outcomes in a sample space and do not share common outcomes

C. Do not have to contain all outcomes in a sample space but do not share common outcomes

D. Do not have to contain all outcomes in a sample space and may share common outcomes

27. The union of events *A* and *B*, denoted by , .

A. Contains all outcomes that are in *A* or *B*

B. Contains all outcomes of an experiment

C. Contains no outcomes that are in *A* and *B*

D. Consists only of outcomes that are in *A* and *B*

28. The intersection of events *A* and *B*, denoted by , .

A. Contains outcomes that are either in *A* or *B*

B. Contains outcomes that are both in *A* and *B*

C. Does not contain outcomes that are either in *A* or *B*

D. Does not contain outcomes that are both in *A* and *B*

29. The intersection of events *A* = {apple pie, peach pie, pumpkin pie} and *B* = {cherry pie, blueberry pie,

pumpkin pie} is .

A. {pumpkin pie}

B. {apple pie, peach pie, cherry pie, blueberry pie}

C. {apple pie, peach pie, pumpkin pie, cherry pie, blueberry pie}

D. {apple pie, peach pie, pumpkin pie, cherry pie, blueberry pie, pumpkin pie}

30. The complement of an event *A*, within the sample space *S*, is the event consisting of .

A. All outcomes in *A* that are in *S*

B. All outcomes in *S* that are in *A*

C. All outcomes in *S* that are not in *A*

D. All outcomes in *A* that are not in *S*

31. For the sample space *S* = {apple pie, cherry pie, peach pie, pumpkin pie}, what is the complement of *A* = {pumpkin pie, cherry pie}?

A. {apple pie}

B. {peach pie}

C. {apple pie, peach pie}

D. {pumpkin pie, cherry pie}

32. Assume the sample space *S* = {win, loss}. Select the choice that fulfills the requirements of the definition of probability.

A. *P*({win}) = 0.7,* P*({loss}) = 0.2

B. *P*({win}) = 0.7,* P*({loss}) = 0.3

C. *P*({win}) = 1.0,* P*({loss}) = 0.1

D. *P*({win}) = 0.5,* P*({loss}) = -0.5

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33. A probability based on logical analysis rather than on observation or personal judgment is *best* referred to

as a(n) .

A. A priori probability

B. Empirical probability

C. Subjective probability

D. None of the above

34. An analyst believes the probability that U.S. stock returns exceed long-term corporate bond returns over a 5-year period is based on personal assessment. This type of probability is *best* characterized as a(n)

.

A. A priori probability

B. Empirical probability

C. Objective probability

D. Subjective probability

35. Which of the following represents a subjective probability?

A. The probability of rolling a 2 on a single die is 1 in 6.

B. Based on a conducted experiment, the probability of tossing a head on an unfair coin is 0.6.

C. A skier believes she has a 10% chance of winning a gold medal.

D. Based on past observation, a manager believes there is a 3-in-5 chance of retaining an employee for at least one year.

36. Which of the following represents an empirical probability?

A. The probability of tossing a head on a coin is 0.5.

B. The probability of rolling a 2 on a single die is 1 in 6.

C. A skier believes she has a 0.10 chance of winning a gold medal.

D. Based on past observation, a manager believes there is a 3-in-5 chance of retaining an employee for at least one year.

37. An analyst has a limit order outstanding on a stock. He argues that the probability that the order will

execute before the close of trading is 0.20. Thus, the odds for the order executing before the close of

trading are .

A. 1 in 4

B. 1 in 5

C. 4 to 1

D. 5 to 1

38. After extensive research, an analyst asserts that there is an 80% chance that ABC Corporation will beat its

EPS forecast. Analogously, the odds for the company beating its EPS forecast are .

A. 1 in 4

B. 1 in 1.25

C. 4 to 1

D. 1.25 to 1

39. The odds for encountering rain on a 500-mile car trip are 3 to 1. What is the probability of rain on this trip?

A. 0.25

B. 0.33

C. 0.50

D. 0.75

40. The odds against winning $1.00 in the lottery are 19 to 1. What is the probability of winning $1.00 in the lottery?

A. 0.05

B. 0.0526

C. 0.90

D. 0.95

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41. An experiment consists of tossing three fair coins. What is the probability of tossing two tails?

A. 1/8

B. 1/4

C. 3/8

D. 1/2

42. Let , and . Calculate .

A. 0.2

B. 0.3

C. 0.9

D. Not enough information to calculate.

43. Given an experiment in which a fair coin is tossed three times, the sample space is *S* = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. Event *A* is defined as tossing one head (H). What is the event *AC* and what is the probability of this event?

A. *AC* = {TTT, HHH, HTH};* P*(*AC*) = 0.375

B. *AC* = {TTT, THH, HHH, HHT};* P*(*AC*) = 0.500

C. *AC* = {TTT, HHH, HHT, HTH, HTT};* P*(*AC*) = 0.625

D. *AC* = {TTT, HHT, HTH, THH, HHH};* P*(*AC*) = 0.625

44. Let , and . Calculate .

A. 0.20

B. 0.33

C. 0.40

D. Not enough information to calculate.

45. Alison has all her money invested in two mutual funds, A and B. She knows that there is a 40% chance that fund A will rise in price, and a 60% chance that fund B will rise in price given that fund A rises in price. What is the probability that both fund A and fund B will rise in price?

A. 0.24

B. 0.40

C. 0.76

D. 1.00

46. Alison has all her money invested in two mutual funds, A and B. She knows that there is a 40% chance that fund A will rise in price, and a 60% chance that fund B will rise in price given that fund A rises in price. There is also a 20% chance that fund B will rise in price. What is the probability that at least one of the funds will rise in price?

A. 0.24

B. 0.36

C. 0.60

D. 0.76

47. Alison has all her money invested in two mutual funds, A and B. She knows that there is a 40% chance that fund A will rise in price, and a 60% chance that fund B will rise in price given that fund A rises in price. There is also a 20% chance that fund B will rise in price. What is the probability that neither fund will rise in price?

A. 0.24

B. 0.36

C. 0.40

D. 0.64

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48. A recent survey shows that the probability of a college student drinking alcohol is 0.6. Further, given that the student is over 21 years old, the probability of drinking alcohol is 0.8. It is also known that 30% of the college students are over 21 years old. The probability of drinking or being over 21 years old is

.

A. 0.24

B. 0.42

C. 0.66

D. 0.90

49. Let and . Suppose *A* and *B* are independent. What is ?

A. 0.12

B. 0.3

C. 0.4

D. 0.7

50.

If *A* and *B* are independent events, then

.

A.

B.

C.

D.

51.

Let *A* and *B* be two independent events with *P*(*A*) = 0.40 and *P*(*B*) = 0.20. Therefore,

.

A.

B.

C.

D.

52. Peter applied to an accounting firm and a consulting firm. He knows that 30% of similarly qualified applicants receive job offers from the accounting firm, while only 20% of similarly qualified applicants receive job offers from the consulting firm. Assume that receiving an offer from one firm is independent of receiving an offer from the other. What is the probability that both firms offer Peter a job?

A. 0.05

B. 0.06

C. 0.44

D. 0.50

53. The likelihood of Company A’s stock price rising is 20 percent, and the likelihood of Company B’s stock price rising is 30 percent. Assume that the returns of Company A and Company B stock are independent

of each other. The probability that the stock price of at least one of the companies will rise is .

A. 6%

B. 10%

C. 44%

D. 50%

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54. Find the missing values marked xx and yy in the following contingency table:

A. xx = 72, yy = 79

B. xx = 27, yy = 77

C. xx = 27, yy = 79

D. xx = 72, yy = 77

55. The contingency table below provides frequencies for the preferred type of exercise for people under the age of 35 and those 35 years of age or older. Find the probability that an individual prefers running.

A. 0.3159

B. 0.3915

C. 0.6085

D. 0.6805

56. The contingency table below provides frequencies for the preferred type of exercise for people under the age of 35, and those 35 years of age or older. Find the probability that an individual prefers biking given that he/she is 35 years old or older.

A. 0.1698

B. 0.1824

C. 0.8175

D. 0.8302

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57. The following probability table shows probabilities concerning Favorite Subject and Gender. What is the probability of selecting an individual who is a female or prefers science?

A. 0.250

B. 0.375

C. 0.625

D. 0.750

58. The following probability table shows probabilities concerning Favorite Subject and Gender. What is the probability of selecting an individual preferring science given that he/she is a female?

A. 0.2609

B. 0.4615

C. 0.5385

D. 0.7391

59. **EXHIBIT** **4-1. **Two hundred people were asked if they had read a book in the last month. The accompanying contingency table, cross-classified by age, is produced.

Refer to Exhibit 4-1. The probability that a respondent is at least 30 years old is *closest* to .

A. 0.33

B. 0.46

C. 0.50

D. 0.65

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60. **EXHIBIT** **4-1. **Two hundred people were asked if they had read a book in the last month. The accompanying contingency table, cross-classified by age, is produced.

Refer to Exhibit 4-1. The probability that a respondent read a book in the last month and is at least 30

years old is *closest* to .

A. 0.12

B. 0.33

C. 0.46

D. 0.88

61. **EXHIBIT** **4-1. **Two hundred people were asked if they had read a book in the last month. The accompanying contingency table, cross-classified by age, is produced.

Refer to Exhibit 4-1. Given that a respondent read a book in the last month, the probability that he/she is

at least 30 years old is *closest* to .

A. 0.33

B. 0.46

C. 0.65

D. 0.88

62. **EXHIBIT** **4-2**. Mark Zuckerberg, the founder of Facebook, has announced that he will eat meat only from animals that he has killed himself (*Vanity Fair*, November 2011). Suppose 257 people were asked: “Does the idea of killing your own food appeal to you, or not?” The accompanying contingency table, cross-classified by gender, is produced from the 187 respondents.

Refer to Exhibit 4-2. The probability that a respondent to the survey is male is *closest* to .

A. 0.19

B. 0.38

C. 0.49

D. 0.64

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63. **EXHIBIT** **4-2**. Mark Zuckerberg, the founder of Facebook, has announced that he will eat meat only from animals that he has killed himself (*Vanity Fair*, November 2011). Suppose 257 people were asked: “Does the idea of killing your own food appeal to you, or not?” The accompanying contingency table, cross-classified by gender, is produced from the 187 respondents.

Refer to Exhibit 4-2. The probability that a respondent is male and feels that the idea of killing his own

food is appealing is *closest* to .

A. 0.19

B. 0.38

C. 0.41

D. 0.59

64. **EXHIBIT** **4-2**. Mark Zuckerberg, the founder of Facebook, has announced that he will eat meat only from animals that he has killed himself (*Vanity Fair*, November 2011). Suppose 257 people were asked: “Does the idea of killing your own food appeal to you, or not?” The accompanying contingency table, cross-classified by gender, is produced from the 187 respondents.

Refer to Exhibit 4-2. Given that the respondent is male, the probability that he feels that the idea of killing

his own food is appealing is *closest* to .

A. 0.19

B. 0.38

C. 0.59

D. 0.64

65. **EXHIBIT** **4-3. **The 150 residents of the town of Wonderland were asked their age and whether they preferred vanilla, chocolate, or swirled frozen yogurt. The results are displayed next.

Refer to Exhibit 4-3. What is the probability that a randomly selected customer prefers vanilla?

A. 0.13

B. 0.27

C. 0.33

D. 0.40

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66. **EXHIBIT** **4-3. **The 150 residents of the town of Wonderland were asked their age and whether they preferred vanilla, chocolate, or swirled frozen yogurt. The results are displayed next.

Refer to Exhibit 4-3. What is the probability a randomly selected customer prefers chocolate given he or she is at least 25 years old?

A. 0.10

B. 0.20

C. 0.27

D. 0.77

67. **EXHIBIT** **4-3. **The 150 residents of the town of Wonderland were asked their age and whether they preferred vanilla, chocolate, or swirled frozen yogurt. The results are displayed next.

Refer to Exhibit 4-3. What is the probability a randomly selected customer prefers chocolate swirled yogurt or is at least 25 years old?

A. 0.10

B. 0.20

C. 0.77

D. 0.90

68. Let , and . Compute .

A. 0.15

B. 0.30

C. 0.45

D. 0.50

69. Let , and . Compute .

A. 0.33

B. 0.45

C. 0.5

D. 0.67

70. Let , , and . Compute .

A. 0.125

B. 0.15

C. 0.20

D. 0.35

71. Let , and . Compute .

A. 0.20

B. 0.50

C. 0.65

D. 0.70

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72. Let , and . Compute .

A. 0.20

B. 0.35

C. 0.57

D. 0.80

73. An analyst expects that 10 percent of all publicly traded companies will experience a decline in earnings next year. The analyst has developed a ratio to help forecast this decline. If the company is headed for a decline, there is a 70% chance that this ratio will be negative. If the company is not headed for a decline, there is only a 20% chance that the ratio will be negative. The analyst randomly selects a company and its

ratio is negative. Based on Bayes’ theorem, the posterior probability that the company will experience a

decline is .

A. 3%

B. 7%

C. 18%

D. 28%

74. An analyst expects that 20 percent of all publicly traded companies will experience a decline in earnings next year. The analyst has developed a ratio to help forecast this decline. If the company is headed for a decline, there is a 90% chance that this ratio will be negative. If the company is not headed for a decline, there is only a 10% chance that the ratio will be negative. The analyst randomly selects a company with

a negative ratio. Based on Bayes’ theorem, the posterior probability that the company will experience a

decline is .

A. 18%

B. 26%

C. 44%

D. 69%

75. Romi, a production manager, is trying to improve the efficiency of his assembly line. He knows that the machine is set up correctly only 60% of the time. He also knows that if the machine is set up correctly, it will produce good parts 80% of the time, but if set up incorrectly, it will produce good parts only 20% of the time. Romi starts the machine and produces one part before he begins the production run. He finds the first part to be good. What is the revised probability that the machine was set up correctly?

A. 48%

B. 56%

C. 86%

D. 96%

76. Romi, a production manager, is trying to improve the efficiency of his assembly line. He knows that the machine is set up correctly only 70% of the time. He also knows that if the machine is set up correctly, it will produce good parts 95% of the time, but if set up incorrectly, it will produce good parts only 40% of the time. Romi starts the machine and produces one part before he begins the production run. He finds the first part to be good. What is the revised probability that the machine was set up correctly?

A. 12%

B. 33.5%

C. 66.5%

D. 84.7%

77. 5! is equal to .

A. 5*4*3*2

B. 5 * 4

C. 5*4*3

D. 5*4*3*2*1

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78. How many ways can a committee of four students be selected from a 15-member club?

A. 15!/44!

B. 15!/(4! × 11!)

C. 15×14×13

D. B and C

79. How many ways can a potential 4-letter word, whether or not it has a meaning, be created out of 10 available different letters?

A. 4*3*2*1

B. 10*9*8*7/(4*3*2)

C. 10*9*8*7*6*5/(4*3*2)

D. 10*9*8*7

80. When some objects are randomly selected, which of the following is true?

A. The order in which objects are selected matters in combinations.

B. The order in which objects are selected does not matter in permutations.

C. The order in which objects are selected does not matter in combinations.

D. The order in which objects are selected matters in both permutations and combinations.

81. A small company that manufactures juggling equipment makes seven different types of clubs. The company wants to start an ad campaign that emphasizes the myriad combinations the avid juggler can create with the company’s clubs. If a juggler wishes to juggle 4 clubs, each of a different type, how many different combinations of the company’s clubs can he or she make?

A. 7

B. 28

C. 35

D. 210

82. Boeing currently produces five models of airplanes for commercial sale. The airline that Lauren works for is rapidly expanding and would like to purchase three airplanes of different models to service various routes. Her job is to analyze which three to buy. How many combinations will she have to analyze?

A. 5

B. 10

C. 15

D. 20

83. How many project teams composed of 5 students can be created out of a class of 10 students?

A. 10

B. 50

C. 252

D. 30,240

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84. The following table summarizes the ages of the 400 richest Americans. Suppose we select one of these individuals. Find the probability that the selected individual is at least 60 years old.

85. The following table summarizes the ages of the 400 richest Americans. Suppose we select one of these individuals. Find the probability that the selected individual is less than 80 years old.

86. An experiment consists of rolling a fair die. Find the probability that we roll a 4 or a 6.

87. An experiment consists of tossing a fair coin and rolling a fair die. Find the probability that we toss a head and roll a 6.

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88. The likelihood of rain has been reported at 80% for next week. Find the odds for rain occurring.

89. Based on his batting average, a baseball player has a 32.7% chance of hitting the ball on his next at-bat. Find the odds against this player getting a hit.

90. Exams are approaching and Helen is allocating time to studying for exams. She feels that with the appropriate amount of studying, she has an 80% chance of getting an A in Marketing. She also feels that she has a 60% chance of getting an A in Spanish with the appropriate amount of studying. Given the demands on her time, she feels that she has only a 45% chance getting an A in both classes. What is the probability that Helen gets an A in at least one of the two classes?

91. Exams are approaching and Helen is allocating time to studying for exams. She feels that with the appropriate amount of studying, she has an 80% chance of getting an A in Marketing. She also feels that she has a 60% chance of getting an A in Spanish with the appropriate amount of studying. Given the demands on her time, she feels that she has only a 45% chance of getting an A in both classes. What is the probability that Helen does not get an A in either class?

92. Exams are approaching and Helen is allocating time to studying for exams. She feels that with the appropriate amount of studying, she has a 70% chance of getting an A, and a 20% chance of getting a B in Marketing. What is the probability that Helen gets an A or a B in Marketing?

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93. Exams are approaching and Helen is allocating time to studying for exams. She plays for the very successful women’s lacrosse team, and must schedule her studying around lacrosse practices and play-off games. The entire team assumes that the probability of making the play-offs is 50%. Helen feels that with the appropriate preparation, she has a 70% chance of getting an A in Marketing, but this chance decreases to 60% if the lacrosse team makes the play-offs. Find the probability of getting an A in Marketing and making the lacrosse play-offs.

94. Exams are approaching and Helen is allocating time to studying for exams. She plays for the very successful women’s lacrosse team, and must schedule her studying around lacrosse practices and play-off games. She feels that with the appropriate preparation, she has a 70% chance of getting an A in Marketing. She also feels that this chance will decrease to 60% if the lacrosse team makes the play-offs. Are getting an A on the exam and being in the lacrosse play-offs independent events? Show evidence of your response.

95. Ryan is hoping to attend graduate school next year. Two of the schools he applied to are the University of Utah and Ohio State University. The probability he gets accepted to Utah given he got accepted to Ohio State is 0.75. The probability he gets accepted to Ohio State is 0.05. The probability he gets accepted to Utah is 0.10. What is the probability he gets accepted to Ohio State given he gets accepted to Utah?

96. Two stocks, A and B, have a historical correlation indistinguishable from zero. The probability that stock A increases next year is 0.2, and the probability that stock B increases next year is 0.4. Calculate the probability that A and B both increase next year.

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97. **EXHIBIT** **4-4. **An investor is keeping a careful eye on the real estate markets in Las Vegas and the Inland Empire. The following are her predictions for the real estate market in 2012.

• With 0.32 probability, foreclosures will increase in Las Vegas.

• With 0.46 probability, foreclosures will increase in Las Vegas or the Inland Empire.

• With 0.27 probability, foreclosures will increase in Las Vegas and the Inland Empire.

Refer to Exhibit 4-4. What is the probability that foreclosures will increase in the Inland Empire?

98. **EXHIBIT** **4-4. **An investor is keeping a careful eye on the real estate markets in Las Vegas and the Inland Empire. The following are her predictions for the real estate market in 2012.

• With 0.32 probability, foreclosures will increase in Las Vegas.

• With 0.46 probability, foreclosures will increase in Las Vegas or the Inland Empire.

• With 0.27 probability, foreclosures will increase in Las Vegas and the Inland Empire.

Refer to Exhibit 4-4. What is the probability that foreclosures will increase in the Inland Empire given that they increased in Vegas?

99. **EXHIBIT** **4-5. **The following contingency table provides frequencies for the preferred type of exercise for people under the age of 35 and those 35 years of age or older. Here xx and yy represent missing values.

Refer to Exhibit 4-5. Compute the probability that an individual is under 35 and prefers running.

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100.**EXHIBIT** **4-5.** The following contingency table provides frequencies for the preferred type of exercise for people under the age of 35 and those 35 years of age or older. Here xx and yy represent missing values.

Refer to Exhibit 4-5. Find the probability that an individual prefers running or biking.

101.**EXHIBIT** **4-5.** The following contingency table provides frequencies for the preferred type of exercise for people under the age of 35 and those 35 years of age or older. Here xx and yy represent missing values.

Refer to Exhibit 4-5. Determine whether selecting an under 35 individual is independent of selecting an individual who prefers swimming.

102.**EXHIBIT** **4-6.** In January of 2012, the second stop for a Republican to get votes toward the presidential nomination was at the New Hampshire Primary. The following exhibit shows the votes several candidates received from registered Republicans and Independents.

Source: *ABC News*

Refer to Exhibit 4-6. What is the probability that a randomly selected voter voted for Ron Paul?

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103.**EXHIBIT** **4-6.** In January of 2012, the second stop for a Republican to get votes toward the presidential nomination was at the New Hampshire Primary. The following exhibit shows the votes several candidates received from registered Republicans and Independents.

Source: *ABC News*

Refer to Exhibit 4-6. Given that a randomly selected voter is not a Republican, what is the probability that he/she voted for Ron Paul?

A. 0.31

B. 0.70

C. 0.52

D. 0.16

104.**EXHIBIT** **4-6.** In January of 2012, the second stop for a Republican to get votes toward the presidential nomination was at the New Hampshire Primary. The following exhibit shows the votes several candidates received from registered Republicans and Independents.

Source: *ABC News*

Refer to Exhibit 4-6. If a randomly selected voter voted for Jon Huntsman, what is the probability he is a Republican?

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105.As part of pharmaceutical testing for drowsiness as a side effect of a drug, 200 patients are randomly assigned to one of two groups of 100 each. One group is given the actual drug and the other a placebo. The number of people who felt drowsy in the next hour is recorded as:

a. What is the probability that a randomly picked patient in the study feels drowsy in the next hour?

b. What is the probability that a randomly picked patient in the study takes the placebo or feels drowsy in the next hour?

c. Given that the patient was given the drug, what is the probability that he/she feels drowsy in the next hour?

d. Is whether a patient feels drowsy independent of taking the drug? Explain using probabilities.

106.Restaurants in London, Paris, and New York want diners to experience eating in pitch darkness to heighten their senses of taste and smell (*Vanity Fair*, December 2011). Suppose 400 people were asked: “If given the opportunity, would you eat at one of these restaurants?” The accompanying contingency table, cross-classified by age, would be produced.

Convert the contingency table to a joint probability table.

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107.Restaurants in London, Paris, and New York want diners to experience eating in pitch darkness to heighten their senses of taste and smell (*Vanity Fair*, December 2011). Suppose 400 people were asked: “If given the opportunity, would you eat at one of these restaurants?” The accompanying contingency table, cross-classified by age, would be produced.

a. What is the probability that a respondent would eat at one of these restaurants?

b. What is the probability that a respondent would eat at one of these restaurants or is in the 30-44 age bracket?

c. Given that the respondent would eat at one of these restaurants, what is the probability that he/she is in the 30-44 age bracket?

d. Is whether a respondent would eat at one of these restaurants independent of one’s age? Explain using probabilities.

108.Members of the saxophone section of a marching band are asked to attend saxophone-only practices once a week. These practices are not mandatory, but they are the only opportunity for the entire section to play together in preparation for the marching season. The section leader has noted that 70% of the section regularly attends practices. Further, given that they attend regularly, there is a 40% chance of earning an A on their performance when later graded by the band director. If they do not attend regularly, there is only a 10% chance of earning an A on their performance. What is the probability that a randomly chosen musician receives an A on their performance?

109.A certain weightlifter is prone to back injury. He finds that he has a 20% chance of hurting his back given he uses the proper form of bending at the hips and keeping his spine locked. The probability he hurts his back with bad form is 95%. The probability he uses proper form is 75%. What is the probability he hurts his back?

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110.Approximately 70% of the state of Pennsylvania sits on a shale formation from which natural gas may be extracted. If a geological test is positive, it has an 80% accuracy rate in correctly identifying a productive drilling site (shale is under the ground). If there is no shale under the ground, geological testing is falsely positive with a probability of 20%. Suppose the result of the geological test comes back positive (the test says there is shale under the ground). It is most important for us to know the probability that there is indeed shale under the ground given a positive geological test result. Find this probability.

111.**EXHIBIT** **4-7.** An investor in Apple is worried the latest management earnings forecast is too aggressive and the company will fall short. His favorite analyst that covers Apple is going to release his report on Apple the week before the earnings announcement. Report stands for the analyst’s report, and Forecast stands for the earnings announcement.

Refer to Exhibit 4-7. What is the probability the earnings announcement is below the forecast?

112.**EXHIBIT** **4-7.** An investor in Apple is worried the latest management earnings forecast is too aggressive and the company will fall short. His favorite analyst that covers Apple is going to release his report on Apple the week before the earnings announcement. Report stands for the analyst’s report, and Forecast stands for the earnings announcement.

Refer to Exhibit 4-7. What is the probability the analyst issued a good report given Apple’s earnings announcement was below the forecast?

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113.A certain state wants to use three letters followed by three digits on their license plates. If each letter and each digit can only be used once, how many possible license plates can be created?

114.A pension plan gives you 12 possible funds to invest in, but you are only allowed to hold four at any given point in time. How many possible combinations of the 12 funds could you have in your portfolio?

115.There are three unfilled seats on a small plane, but 10 people showed up to try to get one of those three unfilled seats. If the airline picks three people at random to get on the plane, what is the probability you and your two kids will get on the plane?

116.A group of students has 12 girls and 10 boys. A project team, including 3 girls and 2 boys, must be created. Find the number of possible project teams.