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
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 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
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 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?