Deck 17: An Introduction to Decision Theory

Question 1

You are trying to decide in which of the three companies you should invest. Refer to the following Payoff Table. If the probability of the market declining in the next year is 0.4, which of the following statements are correct?
i. The Expected Opportunity Loss for Company A is $120.
ii. The Expected Opportunity Loss for Company B is $120.
iii. The Expected Opportunity Loss for Company C is $440.

A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (ii) is a correct statement but not (i) or (iii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Answer 1

(i), (ii), and (iii) are all correct statements.

Question 2

Consider the following decision table in which w, x, y, and z are decision alternatives and A and B are the two possible states of nature, with probabilities 0.40 and 0.60. The expected value for decision X is ___________.

A) 40
B) 75
C) 80
D) 220
E) 30

Answer 2

220

Question 3

You are trying to decide in which of the three companies you should invest. Refer to the following Payoff Table. If the probability of the Market rising in the next year is 0.60, which of the following statements are correct?
i. The Opportunity Loss for Company A is $1,860.
ii. The Opportunity Loss for Company B is $1,860.
iii. The Opportunity Loss for Company C is $1,540.

A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (i) and (ii) are correct statements but not (iii).
E) (i), (ii), and (iii) are all false statements.

Answer 3

(i), (ii), and (iii) are all false statements.

Question 4

You are trying to decide in which of the three companies you should invest. Refer to the following Payoff Table. If the probability of the market declining in the next year is 0.4, which of the following statements are correct?
i. The Expected Opportunity Loss for Company A is $300.
ii. The Expected Opportunity Loss for Company B is $30.
iii. The Expected Opportunity Loss for Company C is $500.

A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (ii) is a correct statement but not (i) or (iii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 5

You are trying to decide in which of the three companies you should invest. Refer to the following Payoff Table. If the probability of the Market rising in the next year is 0.60, which of the following statements are correct?
i. The Expected Monetary Value for Company A is $1,860.
ii. The Expected Monetary Value for Company B is $1,860.
iii. The Expected Monetary Value for Company C is $1,860.

A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (i) and (ii) are correct statements but not (iii).
E) (i), (ii), and (iii) are all false statements.

Question 6

Consider the following decision table in which w, x, y, and z are decision alternatives and A and B are the two possible states of nature, with probabilities 0.40 and 0.60. The expected value for decision Z is ___________.

A) 110
B) 200
C) 170
D) 140
E) 150

Question 7

An investor has a 35% chance of making $1000 and a 65% chance of making $10 000, what is the expected payoff for this investor?

A) $11 000
B) $6 850
C) $7 500
D) $10 000

Question 8

Consider the following decision table in which w, x, y, and z are decision alternatives and A and B are the two possible states of nature, with probabilities 0.40 and 0.60. The expected value for decision W is ___________.

A) 40
B) 75
C) 80
D) 220
E) 30

Question 9

I You are trying to decide in which of the three companies you should invest. Refer to the following Payoff Table. If the market rises in the next year, which of the following statements are correct?
i. The Opportunity Loss for Company A is $200.
ii. The Opportunity Loss for Company B is $200.
ii. The Opportunity Loss for Company C is $700.

A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (ii) is a correct statement but not (i) or (iii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 10

You are trying to decide in which of the three companies you should invest. Refer to the following Payoff Table. If the probability of the Market rising in the next year is 0.50, which of the following statements are correct?
i. The Expected Monetary Value for Company A is $1,450.
ii. The Expected Monetary Value for Company B is $1,960.
iii. The Expected Monetary Value for Company C is $1,500.

A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (i) and (ii) are correct statements but not (iii).
E) (i), (ii), and (iii) are all false statements.

Question 11

You are trying to decide in which of the three companies you should invest. Refer to the following Payoff Table. If the market declines in the next year, which of the following statements are correct?
i. The Opportunity Loss for Company A is $300.
ii. The Opportunity Loss for Company B is $0.
iii. The Opportunity Loss for Company C is $50.

A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (ii) is a correct statement but not (i) or (iii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 12

Below is the payoff table for two stocks based on whether the market rises or declines. Which of the following represents the opportunity loss table?

A)
B)
C)

Question 13

Consider the following decision table in which w, x, y, and z are decision alternatives and A and B are the two possible states of nature, with probabilities 0.40 and 0.60. The expected value for decision Y is ___________.

A) 40
B) 28
C) 50
D) 22
E) 15

Question 14

You are trying to decide in which of the three companies you should invest. Refer to the following Payoff Table. If the probability of the Market rising in the next year is 0.50, which of the following statements are correct?
i. The Expected Monetary Value for Company A is $1,450.
ii. The Expected Monetary Value for Company B is $1,600.
iii. The Expected Monetary Value for Company C is $1,475.

A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (i) and (ii) are correct statements but not (iii).
E) (i), (ii), and (iii) are all false statements.

Question 15

You are trying to decide in which of the three companies you should invest. Refer to the following Payoff Table. If the probability of the Market rising in the next year is 0.60, which of the following statements are correct?
i. The Expected Monetary Value for Company A is $1,860.
ii. The Expected Monetary Value for Company B is $1,860.
iii. The Expected Monetary Value for Company C is $1,540.

A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (i) and (ii) are correct statements but not (iii).
E) (i), (ii), and (iii) are all false statements.

Question 16

A payoff table is needed to:

A) control for possible future events.
B) inform the decision maker of the choices available.
C) compare each combination of decision alternative and state of nature.
D) control for possible future events and inform the decision maker of the choices available.

Question 17

Suppose that the below represents the opportunity loss table for three stocks based on whether the market rises or declines. If there is a 30% chance of the market rising and a 70% chance of it declining, what is the expected opportunity loss for stock C?

A) 490
B) 850
C) 240
D) 910
E) 370

Question 18

The states of nature are:

A) the choices available to the decision maker.
B) the uncontrollable future events.
C) a comparison of each combination of decision alternatives and the state of nature.

Question 19

You are trying to decide in which of the three companies you should invest. Refer to the following Payoff Table. If the market rises in the next year, which of the following statements are correct?
i. The Opportunity Loss for Company A is $200.
ii. The Opportunity Loss for Company B is $200.
iii. The Opportunity Loss for Company C is $200.

A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (ii) is a correct statement but not (i) or (iii).
D) (i) and (ii) are correct statements but not (iii).
E) (i), (ii), and (iii) are all false statements.

Question 20

You are trying to decide in which of the three companies you should invest. Refer to the following Payoff Table. If the market declines in the next year, which of the following statements are correct?
i. The Opportunity Loss for Company A is $300.
ii. The Opportunity Loss for Company B is $30.
iii. The Opportunity Loss for Company C is $500.

A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (ii) is a correct statement but not (i) or (iii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 21

Given the following decision table in which x, y, and z are decision alternatives and A and B are states of nature. Which alternative would be chosen if using the maximax criterion?

A) A
B) B
C) x
D) y
E) z

Question 22

You are trying to decide in which of the three companies you should invest. Refer to the following Payoff Table. If the market rises in the next year, which of the following statements are correct?
i. The Opportunity Loss for Company A is $200.
ii. The Opportunity Loss for Company B is $0.
iii. The Opportunity Loss for Company C is $400.

A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (ii) is a correct statement but not (i) or (iii).
D) (i) and (ii) are correct statements but not (iii).
E) (i), (ii), and (iii) are all false statements.

Question 23

You are trying to decide in which of the three companies you should invest. Refer to the following Payoff Table. If the probability of the market declining in the next year is 0.5, which of the following statements are correct?
i. The Expected value of stock purchased under conditions of certainty is $1,675.
ii. The Expected value of stock purchased under conditions of certainty is $2,200.
iii. The Expected value of stock purchased under conditions of certainty is $1,150.

A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (ii) is a correct statement but not (i) or (iii).
D) (iii) is a correct statement but not (i) or (ii).
E) (i), (ii), and (iii) are all false statements.

Question 24

You are trying to decide in which of the three companies you should invest. Refer to the following Payoff Table. If the market declines in the next year, which of the following statements are correct?
i. The Opportunity Loss for Company A is $250.
ii. The Opportunity Loss for Company B is $30.
iii. The Opportunity Loss for Company C is $500.

A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (ii) is a correct statement but not (i) or (iii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 25

You are trying to decide in which of the three companies you should invest. Refer to the following Payoff Table. If the probability of the market declining in the next year is 0.4, which of the following statements are correct?
i. The Expected value of stock purchased under conditions of certainty is $1,980.
ii. The Expected value of stock purchased under conditions of certainty is $120.
iii. The Expected value of stock purchased under conditions of certainty is $440.

A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (ii) is a correct statement but not (i) or (iii).
D) (iii) is a correct statement but not (i) or (ii).
E) (i), (ii), and (iii) are all false statements.

Question 26

You are trying to decide in which of the three companies you should invest. Refer to the following Payoff Table. If the market declines in the next year, which of the following statements are correct?
i. The Opportunity Loss for Company A is $250.
ii. The Opportunity Loss for Company B is $150.
iii. The Opportunity Loss for Company C is $0.

A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (ii) is a correct statement but not (i) or (iii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 27

A decision tree:

A) uses a box to indicate the point at which a decision must be made.
B) is a picture of all the possible courses of action and the consequentpossible outcomes.
C) contains branches going out from the box which indicate the alternatives under consideration.
D) is a picture of all the possible courses of action and the consequentpossible outcomes, uses a box to indicate the point at which a decision must be made and contains branches going out from the box which indicate the alternatives under consideration.

Question 28

You are trying to decide in which of the three companies you should invest. Refer to the following Payoff Table. If the probability of the Market rising in the next year is 0.50, which of the following statements are correct?
i. The Opportunity Loss for Company A is $1,460.
ii. The Opportunity Loss for Company B is $1,600.
iii. The Opportunity Loss for Company C is $1,475.

A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (i) and (ii) are correct statements but not (iii).
E) (i), (ii), and (iii) are all false statements.

Question 29

You are trying to decide in which of the three companies you should invest. Refer to the following Payoff Table. If the probability of the market declining in the next year is 0.4, which of the following statements are correct?
i. The Expected value of stock purchased under conditions of certainty is $1,980.
ii. The Expected value of perfect information is $120.
iii. The Expected value of perfect information is $180.

A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (ii) is a correct statement but not (i) or (iii).
D) (iii) is a correct statement but not (i) or (ii).
E) (i) and (ii) are correct statements but not (iii).

Question 30

You are trying to decide in which of the three companies you should invest. Refer to the following Payoff Table. If the market rises in the next year, which of the following statements are correct?
i. The Opportunity Loss for Company A is $200.
ii. The Opportunity Loss for Company B is $200.
iii. The Opportunity Loss for Company C is $700.

A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (ii) is a correct statement but not (i) or (iii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 31

You are trying to decide in which of the three companies you should invest. Refer to the following Payoff Table. If the probability of the market declining in the next year is 0.5, which of the following statements are correct?
i. The Expected Opportunity Loss for Company A is $120.
ii. The Expected Opportunity Loss for Company B is $75.
iii. The Expected Opportunity Loss for Company C is $200.

A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (ii) is a correct statement but not (i) or (iii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 32

The maximin strategy:

A) minimizes the maximum gain.
B) maximizes the minimum gain.
C) minimizes the maximum regret.
D) maximizes the minimum regret.

Question 33

You are trying to decide in which of the three companies you should invest. Refer to the following Payoff Table. If the probability of the market declining in the next year is 0.5, which of the following statements are correct?
i. The Expected Opportunity Loss for Company A is $225.
ii. The Expected Opportunity Loss for Company B is $75.
iii. The Expected Opportunity Loss for Company C is $200.

A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (ii) is a correct statement but not (i) or (iii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 34

You are trying to decide in which of the three companies you should invest. Refer to the following Payoff Table. If the probability of the market declining in the next year is 0.5, which of the following statements are correct?
i. The Expected Opportunity Loss for Company A is $20.
ii. The Expected Opportunity Loss for Company B is $75.
iii. The Expected Opportunity Loss for Company C is $440.

A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (ii) is a correct statement but not (i) or (iii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 35

You are trying to decide in which of the three companies you should invest. Refer to the following Payoff Table. If the probability of the market declining in the next year is 0.5, which of the following statements are correct?
i. The Expected value of stock purchased under conditions of certainty is $1,675.
ii. The Expected value of perfect information is $75.
iii. The Expected value of perfect information is $180.

A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (ii) is a correct statement but not (i) or (iii).
D) (iii) is a correct statement but not (i) or (ii).
E) (i) and (ii) are correct statements but not (iii).

Question 36

You are trying to decide in which of the three companies you should invest. Refer to the following Payoff Table. If the probability of the market declining in the next year is 0.5, which of the following statements are correct?
i. The Expected value of stock purchased under conditions of certainty is $1,980.
ii. The Expected value of perfect information is $75.
iii. The Expected value of perfect information is $180.

A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (ii) is a correct statement but not (i) or (iii).
D) (iii) is a correct statement but not (i) or (ii).
E) (i) and (ii) are correct statements but not (iii).

Question 37

The alternative which offers the lowest EOL is the same as the one which

A) offers the highest.
B) maximizes the minimum gain.
C) minimizes the maximum loss.
D) maximizes the maximum gain.

Question 38

Given the following decision table in which x, y, and z are decision alternatives and A and B are states of nature. Which alternative would be chosen if using the maximin criterion?

A) A
B) B
C) x
D) y
E) z

Question 39

i. EVPI = Expected value under conditions of certainty-Optimal decision under conditions of uncertainty.
ii. Three regret strategies that are often used are Maximin, Maximax, and Minimax.
iii. Rankings of the decision alternatives are frequently not highly sensitive to changes in the applied probabilities within a plausible range.

A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 40

You are trying to decide in which of the three companies you should invest. Refer to the following Payoff Table. If the probability of the market declining in the next year is 0.4, which of the following statements are correct?
i. The Expected Opportunity Loss for Company A is $20.
ii. The Expected Opportunity Loss for Company B is $120.
iii. The Expected Opportunity Loss for Company C is $440.

A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (ii) is a correct statement but not (i) or (iii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 41

You have a decision to invest $10,000 in any of four different companies. You estimate the probabilities that the economy will be favourable or unfavourable and you estimate the percent returns over the next year. What is the expected value for Company 4?

A) 5.20%
B) 5.4%
C) 5.6%
D) 9.4%

Question 42

You have a decision to invest $10,000 in any of four different companies. You estimate the probabilities that the economy will be favourable or unfavourable and you estimate the percent returns over the next year. Based on expected opportunity loss, which company do you choose?

A) Company 1
B) Company 2
C) Company 3
D) Company 4

Question 43

You have a decision to invest $10,000 in any of four different companies. You estimate the probabilities that the economy will be favourable or unfavourable and you estimate the percent returns over the next year. What is the expected value for Company 3?

A) 0%
B) 3%
C) -2%
D) 1.2%

Question 44

Given the payoff table below, determine the profit and size of warehouse that would be built, using the maximax criterion.

A) $8 million, small warehouse
B) $5 million, medium warehouse
C) $11 million, large warehouse
D) $15 million, medium warehouse
E) $22 million, large warehouse

Question 45

You have a decision to invest $10,000 in any of four different companies. You estimate the probabilities that the economy will be favourable or unfavourable and you estimate the percent returns over the next year. What is the expected value for Company 1?

A) 9.20%
B) 9%
C) 9.6%
D) 9.4%

Question 46

You have a decision to invest $10,000 in any of four different companies. You estimate the probabilities that the economy will be favourable or unfavourable and you estimate the percent returns over the next year. Which company is chosen using the maximax criterion?

A) Company 1
B) Company 2
C) Company 3
D) Company 4

Question 47

You have a decision to invest $10,000 in any of four different companies. You estimate the probabilities that the economy will be favourable or unfavourable and you estimate the percent returns over the next year. Based on the maximin criterion, what is the choice?

A) Company 1
B) Company 2
C) Company 3
D) Company 4

Question 48

Determine the expected profit for the following distribution.

A) $0
B) $20
C) $30
D) $41

Question 49

You have a decision to invest $10,000 in any of four different companies. You estimate the probabilities that the economy will be favourable or unfavourable and you estimate the percent returns over the next year. Based on expected value, what company do you choose?

A) Company 1
B) Company 2
C) Company 3
D) Company 4

Question 50

Determine the expected opportunity loss for the following payoff table.

A) $0
B) $200
C) $300
D) $500

Question 51

You have a decision to invest $10,000 in any of four different companies. You estimate the probabilities that the economy will be favourable or unfavourable and you estimate the percent returns over the next year. What is the expected value for Company 2?

A) 9.20%
B) 9%
C) 9.6%
D) 9.4%

Question 52

Determine the expected value for the following payoff table.

A) $0
B) $200
C) $300
D) $410

Question 53

Given the payoff table below, determine the expected value and size of warehouse that would be built, given a probability of 0.7 and 0.3 to the high and low demands, respectively.

A) $8 million, small warehouse
B) $5 million, medium warehouse
C) $18.7 million, large warehouse
D) $12 million, medium warehouse
E) $22 million, large warehouse

Question 54

Given the payoff table below, determine the profit and size of warehouse that would be built, using the maximin criterion.

A) $8 million, small warehouse
B) $5 million, medium warehouse
C) $22 million, large warehouse
D) $15 million, medium warehouse