# Chapter 4 If two equally likely events A and B are collectively exhaustive

Document Type

Test Prep

Book Title

Basic Business Statistics 13th Edition

Authors

David M. Levine, Kathryn A. Szabat, Mark L. Berenson

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Basic Probability 4-1

CHAPTER 4: BASIC PROBABILITY

1. If two events are collectively exhaustive, what is the probability that one or the other occurs?

a) 0.

b) 0.50.

c) 1.00.

d) Cannot be determined from the information given.

2. If two events are collectively exhaustive, what is the probability that both occur at the same time?

a) 0.

b) 0.50.

c) 1.00.

d) Cannot be determined from the information given.

3. If two events are mutually exclusive, what is the probability that one or the other occurs?

a) 0.

b) 0.50.

c) 1.00.

d) Cannot be determined from the information given.

4. If two events are mutually exclusive, what is the probability that both occur at the same time?

a) 0.

b) 0.50.

c) 1.00.

d) Cannot be determined from the information given.

4-2 Basic Probability

5. If two events are mutually exclusive and collectively exhaustive, what is the probability that both

occur?

a) 0.

b) 0.50.

c) 1.00.

d) Cannot be determined from the information given.

6. If two events are mutually exclusive and collectively exhaustive, what is the probability that one

or the other occurs?

a) 0.

b) 0.50.

c) 1.00.

d) Cannot be determined from the information given.

7. If events A and B are mutually exclusive and collectively exhaustive, what is the probability that

event A occurs?

a) 0.

b) 0.50.

c) 1.00.

d) Cannot be determined from the information given.

8. If two equally likely events A and B are mutually exclusive and collectively exhaustive, what is

the probability that event A occurs?

a) 0.

b) 0.50.

c) 1.00.

d) Cannot be determined from the information given.

Basic Probability 4-3

9. If two equally likely events A and B are mutually exclusive, what is the probability that event A

occurs?

a) 0.

b) 0.50.

c) 1.00.

d) Cannot be determined from the information given.

10. If two equally likely events A and B are collectively exhaustive, what is the probability that event

A occurs?

a) 0.

b) 0.50.

c) 1.00.

d) Cannot be determined from the information given.

11. Selection of raffle tickets from a large bowl is an example of

a) simple probability.

b) sampling without replacement.

c) subjective probability.

d) None of the above.

12. If two events are independent, what is the probability that they both occur?

a) 0.

b) 0.50.

c) 1.00.

d) Cannot be determined from the information given.

4-4 Basic Probability

13. If the outcome of event A is not affected by event B, then events A and B are said to be

a) mutually exclusive.

b) independent.

c) collectively exhaustive.

d) None of the above.

14. If event A and event B cannot occur at the same time, then events A and B are said to be

a) mutually exclusive.

b) independent.

c) collectively exhaustive.

d) None of the above.

15. If either event A or event B must occur, then events A and B are said to be

a) mutually exclusive.

b) independent.

c) collectively exhaustive.

d) None of the above.

16. The collection of all possible events is called

a) a simple probability.

b) a sample space.

c) a joint probability.

d) the null set.

Basic Probability 4-5

17. All the events in the sample space that are not part of the specified event are called

a) simple events.

b) joint events.

c) the sample space.

d) the complement of the event.

18. Simple probability is also called

a) marginal probability.

b) joint probability.

c) conditional probability.

d) Bayes' theorem.

19. When using the general multiplication rule, P(A and B) is equal to

a) P(A|B)P(B).

b) P(A)P(B).

c) P(B)/P(A).

d) P(A)/P(B).

20. A business venture can result in the following outcomes (with their corresponding chance of

occurring in parentheses): Highly Successful (10%), Successful (25%), Break Even (25%),

Disappointing (20%), and Highly Disappointing (?). If these are the only outcomes possible for

the business venture, what is the chance that the business venture will be considered Highly

Disappointing?

a) 10%

b) 15%

c) 20%

d) 25%

4-6 Basic Probability

21. A survey of banks revealed the following distribution for the interest rate being charged on a

home loan (based on a 30-year mortgage with a 10% down payment) on a certain date in the past.

Interest Rate 3.20%

to

3.29%

3.30%

to

3.39%

3.40%

to

3.49%

3.50%

to

3.59%

3.60%

and

above

Probability 0.12 0.23 0.24 0.35 0.06

If a bank is selected at random from this distribution, what is the chance that the interest rate charged

on a home loan will exceed 3.49%?

a) 0.06

b) 0.41

c) 0.59

d) 1.00

22. The employees of a company were surveyed on questions regarding their educational background

(college degree or no college degree) and marital status (single or married). Of the 600

employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The

probability that an employee of the company is single or has a college degree is:

a) 0.10

b) 0.25

c) 0.667

d) 0.733

23. The employees of a company were surveyed on questions regarding their educational background

(college degree or no college degree) and marital status (single or married). Of the 600

employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The

probability that an employee of the company is married and has a college degree is:

a) 0.0667

b) 0.567

c) 0.667

d) 0.833

Basic Probability 4-7

24. The employees of a company were surveyed on questions regarding their educational background

(college degree or no college degree) and marital status (single or married). Of the 600

employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The

probability that an employee of the company does not have a college degree is:

a) 0.10

b) 0.33

c) 0.67

d) 0.75

25. The probability that house sales will increase in the next 6 months is estimated to be 0.25. The

probability that the interest rates on housing loans will go up in the same period is estimated to be

0.74. The probability that house sales or interest rates will go up during the next 6 months is

estimated to be 0.89. The probability that both house sales and interest rates will increase during

the next 6 months is:

a) 0.10

b) 0.185

c) 0.705

d) 0.90

26. The probability that house sales will increase in the next 6 months is estimated to be 0.25. The

probability that the interest rates on housing loans will go up in the same period is estimated to be

0.74. The probability that house sales or interest rates will go up during the next 6 months is

estimated to be 0.89. The probability that neither house sales nor interest rates will increase

during the next 6 months is:

a) 0.11

b) 0.195

c) 0.89

d) 0.90

4-8 Basic Probability

27. The probability that house sales will increase in the next 6 months is estimated to be 0.25. The

probability that the interest rates on housing loans will go up in the same period is estimated to be

0.74. The probability that house sales or interest rates will go up during the next 6 months is

estimated to be 0.89. The probability that house sales will increase but interest rates will not

during the next 6 months is:

a) 0.065

b) 0.15

c) 0.51

d) 0.89

28. The probability that house sales will increase in the next 6 months is estimated to be 0.25. The

0.74. The probability that house sales or interest rates will go up during the next 6 months is

estimated to be 0.89. The events increase in house sales and increase in interest rates in the next 6

months are

a) independent.

b) mutually exclusive.

c) collectively exhaustive.

d) None of the above.

29. The probability that house sales will increase in the next 6 months is estimated to be 0.25. The

0.74. The probability that house sales or interest rates will go up during the next 6 months is

estimated to be 0.89. The events increase in house sales and no increase in house sales in the next

6 months are

a) independent.

b) mutually exclusive.

c) collectively exhaustive.

d) (b) and (c)

Basic Probability 4-9

30. The probability that a new advertising campaign will increase sales is assessed as being 0.80. The

probability that the cost of developing the new ad campaign can be kept within the original

budget allocation is 0.40. Assuming that the two events are independent, the probability that the

cost is kept within budget and the campaign will increase sales is:

a) 0.20

b) 0.32

c) 0.40

d) 0.88

31. The probability that a new advertising campaign will increase sales is assessed as being 0.80. The

probability that the cost of developing the new ad campaign can be kept within the original

budget allocation is 0.40. Assuming that the two events are independent, the probability that the

cost is kept within budget or the campaign will increase sales is:

a) 0.20

b) 0.32

c) 0.68

d) 0.88

32. The probability that a new advertising campaign will increase sales is assessed as being 0.80. The

probability that the cost of developing the new ad campaign can be kept within the original

budget allocation is 0.40. Assuming that the two events are independent, the probability that the

cost is not kept within budget or the campaign will not increase sales is:

a) 0.12

b) 0.32

c) 0.68

d) 0.88

4-10 Basic Probability

33. The probability that a new advertising campaign will increase sales is assessed as being 0.80. The

probability that the cost of developing the new ad campaign can be kept within the original

budget allocation is 0.40. Assuming that the two events are independent, the probability that

neither the cost is kept within budget nor the campaign will increase sales is:

a) 0.12

b) 0.32

c) 0.68

d) 0.88

34. According to a survey of American households, the probability that the residents own 2 cars if

annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes

over $50,000 and 70% had 2 cars. The probability that the residents of a household own 2 cars

and have an income over $50,000 a year is:

a) 0.12

b) 0.18

c) 0.22

d) 0.48

35. According to a survey of American households, the probability that the residents own 2 cars if

annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes

over $50,000 and 70% had 2 cars. The probability that the residents of a household do not own 2

cars and have an income over $50,000 a year is:

a) 0.12

b) 0.18

c) 0.22

d) 0.48

Basic Probability 4-11

36. According to a survey of American households, the probability that the residents own 2 cars if

annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes

over $50,000 and 70% had 2 cars. The probability that the residents of a household own 2 cars

and have an income less than or equal to $50,000 a year is:

a) 0.12

b) 0.18

c) 0.22

d) 0.48

37. According to a survey of American households, the probability that the residents own 2 cars if

annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes

over $50,000 and 70% had 2 cars. The probability that annual household income is over $50,000

if the residents of a household own 2 cars is:

a) 0.42

b) 0.48

c) 0.50

d) 0.69

38. According to a survey of American households, the probability that the residents own 2 cars if

annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes

over $50,000 and 70% had 2 cars. The probability that annual household income is over $50,000

if the residents of a household do not own 2 cars is:

a) 0.12

b) 0.18

c) 0.40

d) 0.70

4-12 Basic Probability

39. According to a survey of American households, the probability that the residents own 2 cars if

annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes

over $50,000 and 70% had 2 cars. The probability that the residents do not own 2 cars if annual

household income is not over $50,000 is:

a) 0.12

b) 0.18

c) 0.45

d) 0.70

40. A company has 2 machines that produce widgets. An older machine produces 23% defective

widgets, while the new machine produces only 8% defective widgets. In addition, the new

machine produces 3 times as many widgets as the older machine does. Given that a widget was

produced by the new machine, what is the probability it is not defective?

a) 0.06

b) 0.50

c) 0.92

d) 0.94

41. A company has 2 machines that produce widgets. An older machine produces 23% defective

widgets, while the new machine produces only 8% defective widgets. In addition, the new

machine produces 3 times as many widgets as the older machine does. What is the probability

that a randomly chosen widget produced by the company is defective?

a) 0.078

b) 0.1175

c) 0.156

d) 0.310

Basic Probability 4-13

42. A company has 2 machines that produce widgets. An older machine produces 23% defective

widgets, while the new machine produces only 8% defective widgets. In addition, the new

machine produces 3 times as many widgets as the older machine does. Given a randomly chosen

widget was tested and found to be defective, what is the probability it was produced by the new

machine?

a) 0.08

b) 0.15

c) 0.489

d) 0.511

SCENARIO 4-1

Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public

about the harm caused by drunk drivers. A study was recently done that emphasized the problem we

all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were

analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role

in the accident. The numbers are shown below:

Number of Vehicles

Involved

Did alcohol play a role? 1 2 3 Totals

Yes 50 100 20 170

No 25 175 30 230

Totals 75 275 50 400

43. Referring to Scenario 4-1, what proportion of accidents involved more than one vehicle?

a) 50/400 or 12.5%

b) 75/400 or 18.75%

c) 275/400 or 68.75%

d) 325/400 or 81.25%

4-14 Basic Probability

44. Referring to Scenario 4-1, what proportion of accidents involved alcohol and a single vehicle?

a) 25/400 or 6.25%

b) 50/400 or 12.5%

c) 195/400 or 48.75%

d) 245/400 or 61.25%

45. Referring to Scenario 4-1, what proportion of accidents involved alcohol or a single vehicle?

a) 25/400 or 6.25%

b) 50/400 or 12.5%

c) 195/400 or 48.75%

d) 245/400 or 61.25%

46. Referring to Scenario 4-1, given alcohol was involved, what proportion of accidents involved a

single vehicle?

a) 50/75 or 66.67%

b) 50/170 or 29.41%

c) 120/170 or 70.59%

d) 120/400 or 30%

47. Referring to Scenario 4-1, given that multiple vehicles were involved, what proportion of

accidents involved alcohol?

a) 120/170 or 70.59%

b) 120/230 or 52.17%

c) 120/325 or 36.92%

d) 120/400 or 30%

Basic Probability 4-15

48. Referring to Scenario 4-1, given that 3 vehicles were involved, what proportion of accidents

involved alcohol?

a) 20/30 or 66.67%

b) 20/50 or 40%

c) 20/170 or 11.77%

d) 20/400 or 5%

49. Referring to Scenario 4-1, given that alcohol was not involved, what proportion of the accidents

were single vehicle?

a) 50/75 or 66.67%

b) 25/230 or 10.87%

c) 50/170 or 29.41%

d) 25/75 or 33.33%

50. Referring to Scenario 4-1, given that alcohol was not involved, what proportion of the accidents

were multiple vehicle?

a) 50/170 or 29.41%

b) 120/170 or 70.59%

c) 205/230 or 89.13%

d) 25/230 or 10.87%

4-16 Basic Probability

SCENARIO 4-2

An alcohol awareness task force at a Big-Ten university sampled 200 students after the midterm to

ask them whether they went bar hopping the weekend before the midterm or spent the weekend

studying, and whether they did well or poorly on the midterm. The following result was obtained.

Did Well on Midterm Did Poorly on Midterm

Studying for Exam 80 20

Went Bar Hopping 30 70

51. Referring to Scenario 4-2, what is the probability that a randomly selected student who went bar

hopping did well on the midterm?

a) 30/100 or 30%

b) 30/110 or 27.27%

c) 30/200 or 15%

d) (100/200)*(110/200) or 27.50%

52. Referring to Scenario 4-2, what is the probability that a randomly selected student did well on the

midterm or went bar hopping the weekend before the midterm?

a) 30/200 or 15%

b) (80+30)/200 or (30+80)/200 or 55%

c) (30+70)/200 or (70+30)/200 or 50%

d) (80+30+70)/200 or (110+100-30)/200 or 90%

53. Referring to Scenario 4-2, what is the probability that a randomly selected student did well on the

midterm and also went bar hopping the weekend before the midterm?

a) 30/200 or 15%

b) (80+30)/200 or 55%

c) (30+70)/200 or 50%

d) (80+30+70)/200 or 90%

Basic Probability 4-17

54. Referring to Scenario 4-2, the events "Did Well on Midterm" and "Studying for Exam" are

a) dependent.

b) mutually exclusive.

c) collective exhaustive.

d) None of the above.

55. Referring to Scenario 4-2, the events "Did Well on Midterm" and "Studying for Exam" are

a) not dependent.

b) not mutually exclusive.

c) collective exhaustive.

d) None of the above.

56. Referring to Scenario 4-2, the events "Did Well on Midterm" and "Did Poorly on Midterm" are

a) dependent.

b) mutually exclusive.

c) collective exhaustive.

d) All of the above.

57. True or False: When A and B are mutually exclusive, P(A or B) can be found by adding P(A) and

P(B).

58. True or False: The collection of all the possible events is called a sample space.

4-18 Basic Probability

59. True or False: If A and B cannot occur at the same time they are called mutually exclusive.

60. True or False: If either A or B must occur they are called mutually exclusive.

61. True or False: If either A or B must occur they are called collectively exhaustive.

62. True or False: If P(A) = 0.4 and P(B) = 0.6, then A and B must be collectively exhaustive.

63. True or False: If P(A) = 0.4 and P(B) = 0.6, then A and B must be mutually exclusive.

64. True or False: If P(A or B) = 1.0, then A and B must be mutually exclusive.

65. True or False: If P(A or B) = 1.0, then A and B must be collectively exhaustive.

Basic Probability 4-19

66. True or False: If P(A and B) = 0, then A and B must be mutually exclusive.

67. True or False: If P(A and B) = 0, then A and B must be collectively exhaustive.

68. True or False: If P(A and B) = 1, then A and B must be collectively exhaustive.

69. True or False: If P(A and B) = 1, then A and B must be mutually exclusive.

70. Suppose A and B are independent events where P(A) = 0.4 and P(B) = 0.5. Then P(A and B) =

__________.

71. Suppose A and B are mutually exclusive events where P(A) = 0.4 and P(B) = 0.5. Then P(A and

B) = __________.

72. Suppose A and B are mutually exclusive events where P(A) = 0.4 and P(B) = 0.5. Then P(A or B)

= __________.

4-20 Basic Probability

73. Suppose A and B are independent events where P(A) = 0.4 and P(B) = 0.5. Then P(A or B) =

__________.

74. Suppose A and B are events where P(A) = 0.4, P(B) = 0.5, and P(A and B) = 0.1. Then P(A or B)

= __________.

75. Suppose A and B are events where P(A) = 0.4, P(B) = 0.5, and P(A and B) = 0.1. Then P(A|B) =

__________.

76. Suppose A and B are events where P(A) = 0.4, P(B) = 0.5, and P(A and B) = 0.1. Then P(B|A) =

__________.

SCENARIO 4-3

A survey is taken among customers of a fast-food restaurant to determine preference for hamburger or

chicken. Of 200 respondents selected, 75 were children and 125 were adults. 120 preferred hamburger

and 80 preferred chicken. 55 of the children preferred hamburger.

77. Referring to Scenario 4-3, the probability that a randomly selected individual is an adult is

__________.

Basic Probability 4-21

78. Referring to Scenario 4-3, the probability that a randomly selected individual is an adult or a child

is __________.

79. Referring to Scenario 4-3, the probability that a randomly selected individual is a child and

prefers chicken is __________.

80. Referring to Scenario 4-3, the probability that a randomly selected individual is an adult and

prefers chicken is __________.

81. Referring to Scenario 4-3, the probability that a randomly selected individual is a child or prefers

hamburger is __________.

82. Referring to Scenario 4-3, assume we know the person is a child. The probability that this

individual prefers hamburger is __________.

83. Referring to Scenario 4-3, assume we know that a person prefers chicken. The probability that

this individual is an adult is __________.

4-22 Basic Probability

84. Referring to Scenario 4-3, assume we know that a person prefers hamburger. The probability that

this individual is a child is __________.

SCENARIO 4-4

Suppose that patrons of a restaurant were asked whether they preferred water or whether they

preferred soda. 70% said that they preferred water. 60% of the patrons were male. 80% of the males

preferred water.

85. Referring to Scenario 4-4, the probability a randomly selected patron prefers soda is __________.

86. Referring to Scenario 4-4, the probability a randomly selected patron is a female is __________.

87. Referring to Scenario 4-4, the probability a randomly selected patron is a female who prefers soda

is __________.

88. Referring to Scenario 4-4, the probability a randomly selected patron is a female who prefers

water is __________.

Basic Probability 4-23

89. Referring to Scenario 4-4, suppose a randomly selected patron prefers soda. Then the probability

the patron is a male is __________.

90. Referring to Scenario 4-4, suppose a randomly selected patron prefers water. Then the probability

the patron is a male is __________.

91. Referring to Scenario 4-4, suppose a randomly selected patron is a female. Then the probability

the patron prefers water is __________.

92. True or False: Referring to Scenario 4-4, the two events "preferring water" and "preferring soda"

are independent.

93. True or False: Referring to Scenario 4-4, the two events "preferring water" and “being a male” are

independent.

4-24 Basic Probability

SCENARIO 4-5

In a meat packaging plant Machine A accounts for 60% of the plant's output, while Machine B

accounts for 40% of the plant's output. In total, 4% of the packages are improperly sealed. Also, 3%

of the packages are from Machine A and are improperly sealed.

94. Referring to Scenario 4-5, if a package is selected at random, the probability that it will be

properly sealed is ________.

95. Referring to Scenario 4-5, if a package selected at random is improperly sealed, the probability

that it came from machine A is ________.

96. Referring to Scenario 4-5, if a package selected at random came from Machine A, the probability

that it is improperly sealed is ________.

97. Referring to Scenario 4-5, if a package selected at random came from Machine B, the probability

that it is properly sealed is ________.

98. Referring to Scenario 4-5, if a package selected at random came from Machine B, the probability

that it is improperly sealed is ________.

Basic Probability 4-25

SCENARIO 4-6

At a Texas college, 60% of the students are from the southern part of the state, 30% are from the

northern part of the state, and the remaining 10% are from out-of-state. All students must take and

pass an Entry Level Math (ELM) test. 60% of the southerners have passed the ELM, 70% of the

northerners have passed the ELM, and 90% of the out-of-staters have passed the ELM.

99. Referring to Scenario 4-6, the probability that a randomly selected student is someone from

northern Texas who has not passed the ELM is ________.

100. Referring to Scenario 4-6, the probability that a randomly selected student has passed the ELM

is ________.

101. Referring to Scenario 4-6, if a randomly selected student has passed the ELM, the probability

the student is from out-of-state is ________.

102. Referring to Scenario 4-6, if a randomly selected student has not passed the ELM, the

probability the student is from southern Texas is ________.

103. Referring to Scenario 4-6, the probability that a randomly selected student is not from southern

Texas and has not passed the ELM is ________.

4-26 Basic Probability

104. Referring to Scenario 4-6, if a randomly selected student has not passed the ELM, the

probability the student is not from northern Texas is ________.

105. Referring to Scenario 4-6, if a randomly selected student is not from southern Texas, the

probability the student has not passed the ELM is ________.

106. Referring to Scenario 4-6, if a randomly selected student is not from out-of-state, the

probability the student has passed the ELM is ________.

SCENARIO 4-7

The next state lottery will have the following payoffs possible with their associated probabilities.

Payoff Probability

$2.00 0.0500

$25.00 0.0100

$100.00 0.0050

$500.00 0.0010

$5,000.00 0.0005

$10,000.00 0.0001

You buy a single ticket.

107. Referring to Scenario 4-7, the probability that you win any money is ________.

Basic Probability 4-27

108. Referring to Scenario 4-7, the probability that you win at least $100.00 is ________.

109. Referring to Scenario 4-7, if you have a winning ticket, the probability that you win at least

$100.00 is ________.

110. The closing price of a company’s stock tomorrow can be lower, higher or the same as today’s

closed. Without any prior information that may affect the price of the stock tomorrow, the

probability that it will close higher than today’s close is 1/3. This is an example of using which

of the following probability approach?

a) A priori probability

b) Empirical probability

c) Subjective probability

d) Conditional probability

111. The closing price of a company’s stock tomorrow can be lower, higher or the same as today’s

closing price. Based on the closing price of the stock collected over the last month, 25% of the

days the closing price was higher than previous day’s closing price, 45% was lower than previous

day’s and 30% was the same as previous day’s. Based on this information, the probability that

tomorrow’s closing price will be higher than today’s is 25%. This is an example of using which

of the following probability approach?

a) A priori probability

b) Empirical probability

c) Subjective probability

d) Conditional probability

4-28 Basic Probability

112. The closing price of a company’s stock tomorrow can be lower, higher or the same as today’s

closing price. After evaluating all the information available on the company’s fundamentals and

the economic environment, an analyst has determined that the probability that tomorrow’s closing

price will be higher than today’s is determined to be 25%. This is an example of using which of

the following probability approach?

a) A priori probability

b) Empirical probability

c) Subjective probability

d) Conditional probability

SCENARIO 4-8

According to the record of the registrar’s office at a state university, 35% of the students are

freshman, 25% are sophomore, 16% are junior and the rest are senior. Among the freshmen,

sophomores, juniors and seniors, the portion of students who live in the dormitory are, respectively,

80%, 60%, 30% and 20%.

113. Referring to Scenario 4-8, what is the probability that a randomly selected student is a freshman

who lives in a dormitory?

114. Referring to Scenario 4-8, what is the probability that a randomly selected student is a

sophomore who does not live in a dormitory?

115. Referring to Scenario 4-8, what is the probability that a randomly selected student is a junior

who does not live in a dormitory?

Basic Probability 4-29

116. Referring to Scenario 4-8, what is the probability that a randomly selected student is a junior or

senior who lives in a dormitory?

117. Referring to Scenario 4-8, what percentage of the students live in a dormitory?

118. Referring to Scenario 4-8, what percentage of the students do not live in a dormitory?

119. Referring to Scenario 4-8, if a randomly selected student lives in the dormitory, what is the

probability that the student is a freshman?

120. Referring to Scenario 4-8, if a randomly selected student lives in the dormitory, what is the

probability that the student is not a freshman?

121. Referring to Scenario 4-8, if a randomly selected student does not live in the dormitory, what is

the probability that the student is a junior or a senior?

4-30 Basic Probability

122. Referring to Scenario 4-8, determine whether the class status of a student and whether the

student lives in a dormitory are independent.

SCENARIO 4-9

A survey conducted by the Segal Company of New York found that in a sample of 189 large

companies, 40 offered stock options to their board members as part of their non-cash compensation

packages. For small- to mid-sized companies, 43 of the 180 surveyed indicated that they offer stock

options as part of their noncash compensation packages to their board members.

123. Referring to Scenario 4-9, set up a contingency table.

124. Referring to Scenario 4-9, if a company is selected at random, what is the probability that the

company offered stock options to their board members?

125. Referring to Scenario 4-9, if a company is selected at random, what is the probability that the

company is small to mid-sized and did not offer stock options to their board members?

126. Referring to Scenario 4-9, if a company is selected at random, what is the probability that the

company is small to mid-sized or offered stock options to their board members?

Basic Probability 4-31

127. Referring to Scenario 4-9, if a randomly selected company is a large company, what is the

probability that it offered stock options to their board members?

128. Referring to Scenario 4-9, if a randomly selected company offered stock options to their board

members, what is the probability that it is a large company?

129. Referring to Scenario 4-9, is the size of the company independent of whether stock options are

offered to their board members and why?

SCENARIO 4-10

Are whites more likely to claim bias? It was found that 60% of the workers were white, 30% were

black and 10% are other races. Given that a worker was white, the probability that the worker had

claimed bias was 30%. Given that a worker was black, the probability that the worker had claimed

bias was 40%. Given that a worker was other race, the probability that the worker had claimed bias

was 0%.

130. Referring to Scenario 4-10, what is the probability that a randomly selected worker had not

claimed bias?

131. Referring to Scenario 4-10, if a randomly selected worker had claimed bias, what is the

probability that the worker is white?

4-32 Basic Probability

132. Referring to Scenario 4-10, if a randomly selected worker had not claimed bias, what is the

probability that the worker is white?

133. Referring to Scenario 4-10, what is the probability that a randomly selected worker is white and

had claimed bias?

134. Referring to Scenario 4-10, what is the probability that a randomly selected worker is black and

had not claimed bias?

135. Referring to Scenario 4-10, what is the probability that a randomly selected worker is black and

had not claimed bias or is white and has claimed bias?

136. Referring to Scenario 4-10, what is the probability that a randomly selected worker is not black

and had not claimed bias?

137. Referring to Scenario 4-10, when a randomly selected worker was not white, what is the

probability that the worker had not claimed bias?

Basic Probability 4-33

138. You know that the probability of a randomly selected student will cheat on an exam is 1%. You

also know that the probability of a randomly selected student will cheat on an exam knowing that

his/her fellow classmate is cheating on the exam is also 1%. Which of the following is true about

the event of "the randomly selected student cheating on an exam" and "his/her classmate is

cheating on the exam"?

a) They are mutually exclusive.

b) They are collectively exhaustive.

c) They are independent.

d) None of the above.

139. True or False: To ethically advertise a school lottery scheme to try to raise money for the

athletic department, the organizer of the lottery does not need to explicitly specify the probability

of each of the prize in the lottery.

140. True or False: An investment consultant is recommending a certain class of mutual funds to the

clienteles based on its exceptionally high probability of exceptionally high gain. It is an unethical

practice to tell the clienteles the probability of a loss in her recommendations.

141. True or False: An investment consultant is recommending a certain class of mutual funds to the

clienteles based on its exceptionally high probability of gain. It is an ethical practice to explain to

the clienteles what the basis of her probability estimate is.

142. True or False: An investment consultant is recommending a certain class of mutual funds to the

clienteles based on its exceptionally high probability of gain. It is an ethical practice to explain to

the clienteles what the meaning of probability is.

4-34 Basic Probability

143. True or False: An investment consultant is recommending a certain class of mutual funds to the

clienteles based on its exceptionally high probability of gain. It is an unethical practice not to

also recommend a class of mutual funds with an exceptionally high probability of loss.

SCENARIO 4-11

A sample of 300 adults is selected. The contingency table below shows their registration status and

their preferred source of information on current events.

Preferred source of information

Television Newspapers Radio Internet

Voting registration status Registered 45 30 45 36

Not registered 35 44 45 20

144. Referring to Scenario 4-11, if an adult is selected at random, what is the probability that he/she

prefers to get his/her current information from the internet?

145. Referring to Scenario 4-11, if an adult is selected at random, what is the probability that he/she

is a registered voter?

146. Referring to Scenario 4-11, if an adult is selected at random, what is the probability that he/she

is a registered voter who prefers to get his/her current information from the television?

Basic Probability 4-35

147. Referring to Scenario 4-11, if an adult is selected at random, what is the probability that he/she

is a registered voter who does not prefer to get his/her current information from the internet?

148. Referring to Scenario 4-11, if an adult is selected at random, what is the probability that he/she

is a registered voter or prefers to get his/her current information from radio?

149. Referring to Scenario 4-11, if an adult is selected at random, what is the probability that he/she

is a not a registered voter or does not prefer to get his/her current information from the internet?

150. Referring to Scenario 4-11, if a randomly selected adult is a registered voter, what is the

probability that he/she prefers to get his/her current information from the newspapers?

151. Referring to Scenario 4-11, what is the probability that an adult who prefers to get his/her

current information from the internet will be a registered voter?

152. Referring to Scenario 4-11, is the preferred source of current information independent of the

voting registration status?

4-36 Basic Probability

SCENARIO 4-12

Jake woke up late in the morning on the day that he has to go to school to take an important test. He

can either take the shuttle bus which is usually running late 20% of the time or ride his unreliable

motorcycle which breaks down 40% of the time. He decides to toss a fair coin to make his choice.

153. Referring to Scenario 4-12, if Jake, in fact, gets to the test on time, what is the probability that

he took the bus?

154. Referring to Scenario 4-12, if Jake, in fact, gets to the test on time, what is the probability that

he rode his bike?

155. Referring to Scenario 4-12, if Jake is late to the test, what is the probability that he rode his

bike?

156. Referring to Scenario 4-12, if Jake is late to the test, what is the probability that he took the

bus?

157. A new model car from Ford Motor Company offers a keyless entry system that utilizes a four-

letter code. How many different possible combinations are there for the code?

Basic Probability 4-37

158. At the International Pancakes Hut, there are 4 different ways to have an egg cooked, 7 different

choices of pancakes, 5 different types of syrups and 8 different beverages. How many different

ways are there to order an egg, a pancake with a choice of syrup and a beverage?

159. There are 10 finalists at a national dog show. How many different orders of finishing can there

be for all the 10 finalists?

160. Eleven freshmen are to be assigned to eleven empty rooms in a student dormitory. Each room

is considered unique so that it matters who is being assigned to which room. How many different

ways can those eleven freshmen be allocated?

161. There are only 4 empty rooms available in a student dormitory for eleven new freshmen. Each

room is considered unique so that it matters who is being assigned to which room. How many

different ways can those 4 empty rooms be filled one student per room?

162. There are only 4 empty rooms available in a student dormitory for eleven new freshmen. All

the rooms are considered as homogenous so that it does not matter who is being assigned to

which room. How many different ways can those 4 empty rooms be filled one student per room?

4-38 Basic Probability

163. Four freshmen are to be assigned to eleven empty rooms in a student dormitory. All the rooms

are considered as homogenous so that it does not matter who is being assigned to which room.

How many different ways can those 4 freshmen be assigned?

164. There are 47 contestants at a national dog show. How many different ways can contestants fill

the first place, second place, and third place positions?

165. Seven passengers are on a waiting list for an overbooked flight. As a result of cancellations, 3

seats become available. How many different ways can those 3 available seats be filled regardless

of the order?

166. A high school debate team of 4 is to be chosen from a class of 35. How many possible ways

can the team be formed?

167. A debate team of 4 is to be chosen from a class of 35. There are two twin brothers in the class.

How many possible ways can the team be formed which will include only one of the twin

brothers?

168. A debate team of 4 is to be chosen from a class of 35. There are two twin brothers in the class.

How many possible ways can the team be formed which will not include any of the twin

brothers?

Basic Probability 4-39

169. A debate team of 4 is to be chosen from a class of 35. There are two twin brothers in the class.

How many possible ways can the team be formed which will include both of the twin brothers?

170. An exploration team of 2 women and 3 men is to be chosen from a candidate pool of 6 women

and 7 men. How many different ways can this team of 5 be formed?

171. Twelve students in a Business Statistics class are to be formed into three teams of four. How

many different ways can this be done?

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