Chapter 15: DECISIONS UNDER RISK AND UNCERTAINTY
Chapter 15: DECISIONS UNDER RISK AND UNCERTAINTY
Multiple Choice
15-1 A probability distribution
a. is a way of dealing with uncertainty.
b. lists all possible outcomes and the corresponding probabilities of occurrence.
c. shows only the most likely outcome in an uncertain situation.
d. both a and b
e. both a and c
15-2 The variance of a probability distribution is used to measure risk because a higher variance is
associated with
a. a wider spread of values around the mean.
b. a more compact distribution.
c. a lower expected value.
d. both a and b
e. all of the above
15-3 Risk exists when
a. all possible outcomes are known but probabilities can’t be assigned to the outcomes.
b. all possible outcomes are known and probabilities can be assigned to each.
c. all possible outcomes are known but only objective probabilities can be assigned to each.
d. future events can influence the payoffs but the decision maker has some control over their
probabilities.
e. c and d
15-4 When a manager can list all outcomes and assign probabilities to each
a. uncertainty exists.
b. both risk and uncertainty exist.
c. risk exists.
d. the manager should use the minimax rule for making a decision.
e. b and d
Chapter 15: DECISIONS UNDER RISK AND UNCERTAINTY
15-5 Subjective probabilities are
a. determined from actual data on part experiences.
b. used in the presence of uncertainty.
c. almost never used from decision making.
d. based on feelings or hunches.
e. c and d
15-6 Choosing the decision with the maximum possible payoff
a. is the maximax rule.
b. ignores possible bad outcomes.
c. is a guide for decision making under uncertainty.
d. all of the above
e. none of the above
15-7 The maximin rule
a. ignores bad outcomes.
b. is used by optimistic managers.
c. minimizes the potential regret.
d. a and c
e. none of the above
15-8 Using the minimax regret rule the manager makes the decision
a. with the smallest worst−potential regret.
b. with the largest worst−potential regret.
c. knowing he will not regret it.
d. that has the highest expected value relative to the other decisions.
Chapter 15: DECISIONS UNDER RISK AND UNCERTAINTY
15-9 In making decisions under risk
a. maximizing expected value is always the best rule.
b. mean variance analysis is always the best rule.
c. the coefficient of variation rule is always best.
d. maximizing expected value is best for making repeated decisions with identical
probabilities.
e. none of the above
15-10 A firm is considering two projects, A and B, with the following probability distributions for profit.
Profit
($1,000s)
Project A
Probability (%)
Project B
Probability (%)
$ 20
40
60
80
100
10
15
50
15
10
10
15
25
40
10
Given the above, the expected value of project A (in $1,000s) is
a. $60
b. $65
c. $70
d. $75
e. $80
15-11 A firm is considering two projects, A and B, with the following probability distributions for profit.
Profit
($1,000s)
Project A
Probability (%)
Project B
Probability (%)
$ 20
40
60
10
15
50
10
15
25
Chapter 15: DECISIONS UNDER RISK AND UNCERTAINTY
80
100
15
10
40
10
Given the above, the variance of project A is
a. 7.07
b. 50
c. 440
d. 4,000
e. 380
15-12 A firm is considering two projects, A and B, with the following probability distributions for profit.
Profit
($1,000s)
Project A
Probability (%)
Project B
Probability (%)
$ 20
40
60
80
100
10
15
50
15
10
10
15
25
40
10
Given the above, what is the expected value of project B (in $1,000s)?
a. $60
b. $65
c. $70
d. $75
e. $80
15-13 A firm is considering two projects, A and B, with the following probability distributions for profit.
Profit
($1,000s)
Project A
Probability (%)
Project B
Probability (%)
$ 20
40
60
80
100
10
15
50
15
10
10
15
25
40
10
Chapter 15: DECISIONS UNDER RISK AND UNCERTAINTY
Given the above, what is the variance of project B?
a. 10
b. 21
c. 165
d. 440
e. 515
15-14 A firm is considering two projects, A and B, with the following probability distributions for profit.
Profit
($1,000s)
Project A
Probability (%)
Project B
Probability (%)
$ 20
40
60
80
100
10
15
50
15
10
10
15
25
40
10
Given the above, a decision maker using the coefficient of variation rule would
a. choose project A.
b. choose project A only if risk averse.
c. choose project B.
d. choose project B only if risk loving.
e. not be able to make a decision using that rule.
15-15 A firm is considering two projects, A and B, with the following probability distributions for profit.
Profit
($1,000s)
Project A
Probability (%)
Project B
Probability (%)
$ 20
40
60
80
100
10
15
50
15
10
10
15
25
40
10
Given the above, a decision maker who is risk neutral would
a. choose project A.
b. choose project B.
Chapter 15: DECISIONS UNDER RISK AND UNCERTAINTY
c. not be able to make a decision.
d. change probabilities because no decision maker is ever risk neutral.
15-16 A firm is considering two projects, A and B, with the following probability distributions for profit.
Profit
($1,000s)
Project A
Probability (%)
Project B
Probability (%)
$20406080100
se
10
15
50
15
10
10
15
25
40
10
Given the above, the coefficient of variation (to 2 decimal places) is
a. higher for A.
b. higher for B.
c. equal for the two.
d. unable to be used for this choice.
e. both c and d
15-17 In the maximin strategy, a manager choosing between two options will choose the option that:
a. has the highest expected profit
b. provides the best of the worst possible outcomes
c. minimizes the maximum loss
d. both a and b
e. both b and c
15-18 In the maximax strategy a manager choosing between two options will choose the option that
a. has the highest expected profit.
b. provides the best of the worst possible outcomes.
c. provides the best of the highest possible outcomes.
d. has the lowest variance.
e. a and d
15-19 Refer to the following probability distribution for profit to answer the question below:
Profit
Probability
$30
40
50
60
0.05
0.25
0.60
0.10
What is the expected profit for this distribution?
a. $11,875
b. $46
c. $47.50
d. $48.75
15-20 Refer to the following probability distribution for profit to answer the question below:
Profit
Probability
$30
40
50
60
0.05
0.25
0.60
0.10
What is the variance of this distribution?
a. 48.75
b. 2,376
c. 525
d. 70
e. 11.875
Chapter 15: DECISIONS UNDER RISK AND UNCERTAINTY
15-21 Refer to the following probability distribution for profit to answer the question below:
Profit
Probability
$30
40
50
60
0.05
0.25
0.60
0.10
What is the coefficient of variation for this distribution?
a. 1.67
b. 0.675
c. 18.6
d. 0.147
e. 1.03
15-22 The following payoff matrix shows the various profit outcomes for 3 projects, A, B, and C, under
2 possible states of nature: the product price is $10 or the product price is $20.
Profit
P = $10
P = $20
20
80
40
60
−26
140
Using the maximax rule, the decision maker would choose
a. A.
b. B.
c. C.
d. impossible to say from the information given
15-23 The following payoff matrix shows the various profit outcomes for 3 projects, A, B, and C, under
2 possible states of nature: the product price is $10 or the product price is $20.
Profit
P = $10
P = $20
20
80
40
60
−26
140
Chapter 15: DECISIONS UNDER RISK AND UNCERTAINTY
Using the maximin rule, the decision maker would choose
a. A.
b. B.
c. C.
d. either A or B because neither has negative profit
15-24 The following payoff matrix shows the various profit outcomes for 3 projects, A, B, and C, under
2 possible states of nature: the product price is $10 or the product price is $20.
Profit
P = $10
P = $20
20
80
40
60
−26
140
Using the maximum expected value rule, the decision maker would choose
a. A.
b. B.
c. C.
d. impossible to tell from the information
15-25 The following payoff matrix shows the various profit outcomes for 3 projects, A, B, and C, under
2 possible states of nature: the product price is $10 or the product price is $20.
Profit
P = $10
P = $20
20
80
40
60
−26
140
Using the equal probability rule the decision maker would choose
a. A.
b. B.
c. C.
d. impossible to tell from information
Chapter 15: DECISIONS UNDER RISK AND UNCERTAINTY
15-26 The following payoff matrix shows the various profit outcomes for 3 projects, A, B, and C, under
2 possible states of nature: the product price is $10 or the product price is $20.
Profit
P = $10
P = $20
20
80
40
60
−26
140
Using the minimax regret rule the decision maker would choose
a. A.
b. B.
c. C.
d. impossible to tell from the information
15-27 The following payoff matrix shows the profit outcomes for three projects, A, B, and C, for each
of two possible product prices. There is a 60% probability the price will be $10 and a 40%
probability the price will be $20.
Profit
P = $10
P = $20
20
80
40
60
−26
140
Using the maximum expected value rule a decision maker would choose
a. A.
b. B.
c. C.
d. impossible to tell from the information
Chapter 15: DECISIONS UNDER RISK AND UNCERTAINTY
15-28 The following payoff matrix shows the profit outcomes for three projects, A, B, and C, for each
of two possible product prices. There is a 60% probability the price will be $10 and a 40%
probability the price will be $20.
Profit
P = $10
P = $20
20
80
40
60
−26
140
Using the mean variance rule a decision maker would choose
a. A.
b. B.
c. C.
d. can’t use this rule under these circumstances
15-29 A firm making production plans believes there is a 30% probability the price will be $10, a 50%
probability the price will be $15, and a 20% probability the price will be $20. The manager must
decide whether to produce 6,000 units of output (A), 8,000 units (B) or 10,000 units (C). The
following table shows 9 possible outcomes depending on the output chosen and the actual price.
Profit (Loss) when price is
Production
6,000 (A)
8,000 (B)
10,000 (C)
$10
−$200
−$400
−$1,000
$15
$400
$600
$800
$20
$1,000
$1,600
$3,000
What is the expected profit if 6,000 units are produced?
a. $171
b. $840
c. $640
d. $340
e. $260
Chapter 15: DECISIONS UNDER RISK AND UNCERTAINTY
15-30 A firm making production plans believes there is a 30% probability the price will be $10, a 50%
probability the price will be $15, and a 20% probability the price will be $20. The manager must
decide whether to produce 6,000 units of output (A), 8,000 units (B) or 10,000 units (C). The
following table shows 9 possible outcomes depending on the output chosen and the actual price.
Profit (Loss) when price is
Production
6,000 (A)
8,000 (B)
10,000 (C)
$10
−$200
−$400
−$1,000
$15
$400
$600
$800
$20
$1,000
$1,600
$3,000
What is the expected profit if 10,000 units are produced?
a. $500
b. $700
c. $625
d. $1,000
e. $1,754
15-31 A firm making production plans believes there is a 30% probability the price will be $10, a 50%
probability the price will be $15, and a 20% probability the price will be $20. The manager must
decide whether to produce 6,000 units of output (A), 8,000 units (B) or 10,000 units (C). The
following table shows 9 possible outcomes depending on the output chosen and the actual price.
Profit (Loss) when price is
Production
6,000 (A)
8,000 (B)
10,000 (C)
$10
−$200
−$400
−$1,000
$15
$400
$600
$800
$20
$1,000
$1,600
$3,000
If the mean-variance rule is used, how much should the firm produce?
a. 6,000
b. 8,000
c. 10,000
d. cannot use this rule to make the decision
Chapter 15: DECISIONS UNDER RISK AND UNCERTAINTY
15-32 A firm making production plans believes there is a 30% probability the price will be $10, a 50%
probability the price will be $15, and a 20% probability the price will be $20. The manager must
decide whether to produce 6,000 units of output (A), 8,000 units (B) or 10,000 units (C). The
following table shows 9 possible outcomes depending on the output chosen and the actual price.
Profit (Loss) when price is
Production
6,000 (A)
8,000 (B)
10,000 (C)
$10
−$200
−$400
−$1,000
$15
$400
$600
$800
$20
$1,000
$1,600
$3,000
What is the variance if 6,000 units are produced?
a. 490,000
b. 176,400
c. 100,000
d. 68,200
e. 76,460
15-33 A firm making production plans believes there is a 30% probability the price will be $10, a 50%
probability the price will be $15, and a 20% probability the price will be $20. The manager must
decide whether to produce 6,000 units of output (A), 8,000 units (B) or 10,000 units (C). The
following table shows 9 possible outcomes depending on the output chosen and the actual price.
Profit (Loss) when price is
Production
6,000 (A)
8,000 (B)
10,000 (C)
$10
−$200
−$400
−$1,000
$15
$400
$600
$800
$20
$1,000
$1,600
$3,000
For the above payoff matrix, suppose the manager has no idea about the probability of any of the
three prices occurring. If the maximax rule is used how much will the firm produce?
a. 6,000
b. 8,000
c. 10,000
d. cannot use this rule to make the decision