Deck 21: Decision Analysis

Question 1

Future events that cannot be controlled by the decision maker are called

A)indicators
B)states of nature
C)prior probabilities
D)posterior probabilities

Answer 1

B

Question 2

A graphic presentation of the expected gain from the various options open to the decision maker is called

A)a payoff table
B)a decision tree
C)the expected opportunity loss
D)the expected value of perfect information

Answer 2

B

Question 3

Nodes indicating points where an uncertain event will occur are known as

A)decision nodes
B)chance nodes
C)marginal nodes
D)conditional nodes

Answer 3

B

Question 4

The efficiency of information is the ratio of

A)EOL to EVSI
B)EOL to EVPI
C)EVPI to EVSI
D)EVSI to EVPI

Question 5

An intersection or junction point of a decision tree is called a (n)

A)junction
B)intersection
C)intersection point
D)node

Question 6

The probability of the states of nature,after use of Bayes' theorem to adjust the prior probabilities based upon given indicator information,is called

A)marginal probability
B)conditional probability
C)posterior probability
D)None of these alternatives is correct.

Question 7

New information obtained through research or experimentation that enables an updating or revision of the state-of-nature probabilities is

A)population information
B)sampling without replacement
C)sample information
D)conditional information

Question 8

The expected opportunity loss of the best decision alternative is the

A)expected monetary value
B)payoff
C)expected value of perfect information
D)None of these alternatives is correct.

Question 9

The probability of both sample information and a particular state of nature occurring simultaneously is

A)unconditional probability
B)joint probability
C)marginal probability
D)conditional probability

Question 10

A tabular presentation of the expected gain from the various options open to a decision maker is called

A)a payoff table
B)a decision tree
C)the expected opportunity loss
D)the expected value of perfect information

Question 11

In computing an expected value (EV),the weights are

A)decision alternative probabilities
B)in pounds or some unit of weight
C)in dollars or some units of currency
D)the state-of-nature probabilities

Question 12

The probability of one event given the known outcome of a (possibly)related event is known as

A)unconditional probability
B)joint probability
C)marginal probability
D)conditional probability

Question 13

The result obtained when a decision alternative is chosen and a chance event occurs is known as

A)happenstance
B)consequence
C)alternative probability
D)conditional probability

Question 14

The uncontrollable future events that can affect the outcome of a decision are known as

A)alternatives
B)decision outcome
C)payoff
D)states of nature

Question 15

Nodes indicating points where a decision is made are known as

A)decision nodes
B)chance nodes
C)marginal nodes
D)conditional nodes

Question 16

A decision criterion which weights the payoff for each decision by its probability of occurrence is known as the

A)Payoff criterion
B)expected value criterion
C)probability
D)expected value of perfect information

Question 17

An uncertain future event affecting the consequence,or payoff,associated with a decision is known as

A)unconditional probability
B)unknown probability
C)chance event
D)uncertain probability

Question 18

For a decision alternative,the weighted average of the payoffs is known as

A)the expected value of perfect information
B)the expected value
C)the expected probability
D)perfect information

Question 19

A line or arc connecting the nodes of a decision tree is called a(n)

A)junction
B)intersection
C)branch
D)node

Question 20

A tabular representation of the payoffs for a decision problem is a

A)decision tree
B)payoff table
C)matrix
D)sequential matrix

Question 21

The process of revising prior probabilities to create posterior probabilities based on sample information is a

A)revision process
B)sampling revision
C)Bayesian revision
D)posterior revision

Question 22

Exhibit 21-3
Below you are given a payoff table involving two states of nature and three decision alternatives.
The probability of the occurrence of state of nature S₁ is 0.4.
Refer to Exhibit 21-3.The recommended decision based on the expected monetary value criterion is

A)A
B)B
C)C
D)All alternatives are the same.

Question 23

Exhibit 21-2
Below you are given a payoff table involving three states of nature and two decision alternatives.
The probability that S₁ will occur is 0.1;the probability that S₂ will occur is 0.6.
Refer to Exhibit 21-2.The expected value of perfect information equals

A)12
B)4
C)37
D)29

Question 24

Exhibit 21-1
Below you are given a payoff table involving two states of nature and three decision alternatives.
The probability of occurrence of S₁ = 0.2.
Refer to Exhibit 21-1.The recommended decision alternative based on the expected monetary value is

A)A
B)B
C)C
D)All alternatives are the same.

Question 25

The difference between the expected value of an optimal strategy based on sample information and the "best" expected value without any sample information is called the

A)optimal information
B)expected value of sample information
C)expected value of perfect information
D)efficiency of information

Question 26

Exhibit 21-2
Below you are given a payoff table involving three states of nature and two decision alternatives.
The probability that S₁ will occur is 0.1;the probability that S₂ will occur is 0.6.
Refer to Exhibit 21-2.The recommended decision based on the expected value criterion is

A)A
B)B
C)Both alternatives are the same.
D)None of these alternatives is correct.

Question 27

The probabilities of states of nature after revising the prior probabilities based on given indicator information are

A)the expected probabilities
B)the posterior probabilities
C)the prior probabilities

Question 28

Prior probabilities are the probabilities of the states of nature

A)after obtaining sample information
B)prior to obtaining of perfect information
C)prior to obtaining sample information
D)after obtaining perfect information

Question 29

Exhibit 21-4
Below you are given a payoff table involving two states of nature and three decision alternatives.
The probability of the occurrence of S₁ = 0.3.
Refer to Exhibit 21-4.The expected monetary value of alternative C is

A)10.2
B)13.2
C)12.9
D)26

Question 30

Exhibit 21-3
Below you are given a payoff table involving two states of nature and three decision alternatives.
The probability of the occurrence of state of nature S₁ is 0.4.
Refer to Exhibit 21-3.The expected value of perfect information equals

A)13,000
B)14,000
C)15,000
D)16,000

Question 31

Exhibit 21-3
Below you are given a payoff table involving two states of nature and three decision alternatives.
The probability of the occurrence of state of nature S₁ is 0.4.
Refer to Exhibit 21-3.The expected monetary value of the best alternative equals

A)13,000
B)14,000
C)15,000
D)16,000

Question 32

Exhibit 21-4
Below you are given a payoff table involving two states of nature and three decision alternatives.
The probability of the occurrence of S₁ = 0.3.
Refer to Exhibit 21-4.The expected value of the best alternative is

A)12.9
B)13.2
C)10.2
D)28.0

Question 33

Exhibit 21-4
Below you are given a payoff table involving two states of nature and three decision alternatives.
The probability of the occurrence of S₁ = 0.3.
Refer to Exhibit 21-4.The recommended decision alternative based on the expected monetary value is

A)A
B)B
C)C
D)None of these alternatives is correct.

Question 34

Information about a state of nature is known as

A)natural information
B)states information
C)a sampling method
D)an indicator

Question 35

Exhibit 21-1
Below you are given a payoff table involving two states of nature and three decision alternatives.
The probability of occurrence of S₁ = 0.2.
Refer to Exhibit 21-1.The expected monetary value of the best alternative is

A)8.8
B)7.4
C)9.6
D)11.6

Question 36

Exhibit 21-4
Below you are given a payoff table involving two states of nature and three decision alternatives.
The probability of the occurrence of S₁ = 0.3.
Refer to Exhibit 21-4.The expected value of perfect information is

A)1.5
B)1.2
C)1.0
D)4.8

Question 37

The expected value of information that would tell the decision maker exactly which state of nature is going to occur is

A)the expected value of sample information
B)the expected value of perfect information
C)the maximum information
D)the expected value

Question 38

Exhibit 21-1
Below you are given a payoff table involving two states of nature and three decision alternatives.
The probability of occurrence of S₁ = 0.2.
Refer to Exhibit 21-1.The expected monetary value of alternative A is

A)7.4
B)11.6
C)8.8
D)13

Question 39

Exhibit 21-1
Below you are given a payoff table involving two states of nature and three decision alternatives.
The probability of occurrence of S₁ = 0.2.
Refer to Exhibit 21-1.The expected value of perfect information is

A)6.2
B)2.0
C)13.6
D)4.8

Question 40

Exhibit 21-2
Below you are given a payoff table involving three states of nature and two decision alternatives.
The probability that S₁ will occur is 0.1;the probability that S₂ will occur is 0.6.
Refer to Exhibit 21-2.The expected value of the best alternative equals

A)29
B)105
C)12
D)38.5

Question 41

Assume you are faced with the following decision alternatives and two states of nature.The probability of the occurrence of state of nature 1 is 0.35.The payoff table is shown below.

a.Determine the expected value of each alternative and indicate which decision alternative is the best.
b.Determine the expected value with perfect information about the states of nature.
c.Determine the expected value of perfect information.

Question 42

A fashion designer wants to produce a new line of clothes.In the production of the clothes,expensive,medium-priced,or inexpensive materials can be used.The profits associated with each type of material depend upon economic conditions next year.Below you are given the payoff table.

An economist believes that the probability that the economy will improve is 20%,the probability that the economy will stay the same is 70%,and the probability that the economy will get worse is 10%.
a.Compute the expected monetary value for each decision.Which decision is the best?
b.Compute the expected value of perfect information.

Question 43

Michael,Nancy,& Associates (MNA)produce color printers.The demand for their printers could be light,medium,or high with the following probabilities.

The company has three production alternatives for the coming period.The payoffs (in millions of dollars)associated with the three alternatives are shown below.

a.Compute the expected value of the three alternatives.Which alternative would you select,based on the expected values?
b.Compute the expected value with perfect information (i.e. ,expected value under certainty).
c.Compute the expected value of perfect information (EVPI).

Question 44

Assume you have a sum of money available that you would like to invest in one of the three available investment plans: stocks,bonds,or money market.The conditional payoffs of each plan under two possible economic conditions are shown below.The probability of the occurrence of economic condition I is 0.28.

a.Compute the expected value of the three investment options.Which investment option would you select,based on the expected values?
b.Compute the expected value with perfect information (i.e. ,expected value under certainty).
c.Compute the expected value of perfect information (EVPI).

Question 45

Below you are given a payoff table involving two states of nature and two decision alternatives.

The probability of the occurrence of S₁ is 0.3.
a.Compute the expected monetary value for each decision.Which decision is the best?
b.Compute the expected value of perfect information.

Question 46

Exhibit 21-5
Below you are given a payoff table involving three states of nature and three decision alternatives.
The probability of occurrence of S₁ is 0.2 and the probability of occurrence of S₂ is 0.3.
Refer to Exhibit 21-5.The expected monetary value of alternative C is

A)30
B)6.5
C)5.7
D)5.5

Question 47

A group of investors wants to open up a jewelry store in a new shopping center.The investors are trying to decide whether to stock the store with inexpensive jewelry,medium-priced jewelry,or expensive jewelry.The probability of their choice depends upon the economic conditions.The payoff table below gives the anticipated profits for different states of the economy.The probability of prosperity is 0.5.

a.Determine the expected value of each alternative and indicate which decision alternative is the best.
b.Determine the expected value with perfect information about the states of nature.
c.Determine the expected value of perfect information.

Question 48

Suppose we are interested in investing in one of three investment opportunities: d₁,d₂,or d₃.The following profit payoff table shows the profits (in thousands of dollars)under each of the 3 possible economic conditions-S₁,S₂,and S₃.

Assume the states of nature have the following probabilities of occurrence.

a.Determine the expected value of each alternative and indicate which decision alternative is the best.
b.Determine the expected value with perfect information about the states of nature.
c.Determine the expected value of perfect information.

Question 49

Exhibit 21-5
Below you are given a payoff table involving three states of nature and three decision alternatives.
The probability of occurrence of S₁ is 0.2 and the probability of occurrence of S₂ is 0.3.
Refer to Exhibit 21-5.The expected monetary value of the best alternative is

A)5.0
B)6.5
C)7.5
D)9.0

Question 50

An investor has a choice between four investments.The profitability of the investments depends upon the market.The payoff table is given below for different market conditions.

a.A market economist has stated that there is a 25% chance that the market will stay the same,a 35% chance that the market will decrease,and a 40% chance that the market will increase.Compute the expected monetary value for each investment.Which investment is the best?
b.Compute the expected value of perfect information.

Question 51

Exhibit 21-5
Below you are given a payoff table involving three states of nature and three decision alternatives.
The probability of occurrence of S₁ is 0.2 and the probability of occurrence of S₂ is 0.3.
Refer to Exhibit 21-5.The expected value of perfect information is

A)18.2
B)11.7
C)51
D)37

Question 52

The owner of a new gourmet kitchenware shop wishes to determine how many days and evenings to keep the shop open.The various payoffs (in $1,000s)are indicated in the table below.

Assume the probabilities of the three states of nature are P(S₁)= 0.60,P(S₂)=0 .30,and P(S₃)= 0.1.
a.Determine the expected value of each alternative and indicate which decision alternative is the best.
b.Determine the expected value with perfect information about the states of nature.
c.Determine the expected value of perfect information.

Question 53

An automobile manufacturer must make an immediate decision on the car size that should account for the majority of the firm's production two years from now.The firm perceives three possible states of nature at that time: S1,gasoline will be rationed;S2,gasoline will be readily available at close to current prices;and S3,gasoline will be readily available,but at much higher prices.The firm has determined the following profit payoff table (in $1,000s).

a.An economist at the auto company has advised the firm that the probabilities of the states of nature are P(S₁)= .2,P(S₂)= .5,and P(S₃)= .3.Find the expected monetary value for the three decisions.
b.Which decision should be chosen under the expected monetary value criterion?
c.Determine the expected value of perfect information.

Question 54

Exhibit 21-5
Below you are given a payoff table involving three states of nature and three decision alternatives.
The probability of occurrence of S₁ is 0.2 and the probability of occurrence of S₂ is 0.3.
Refer to Exhibit 21-5.The recommended decision alternative based on the expected monetary value is

A)A
B)B
C)C
D)All alternatives are the same.

Question 55

You are given the following payoff table.

Assume the following probability information is given.

a.Find the values of P(I₁)and P(I₂).
b.What are the values of P(S₁|I₁),P(S₂|I₁),P(S₁|I₂),and P(S₂|I₂)?
c.Use the decision tree approach and determine the optimal decision strategy.What is the expected value of the solution?
d.Determine the expected value of sample information.

Question 56

The following payoff table shows profits for two decision alternatives under three different states of nature.It is known that the probability of the occurrence of state of nature 1 is 0.1.

a.What should the probabilities of states of natures 2 and 3 be so that the expected values of the two decision alternatives equal one another?
b.Determine the expected values.

Question 57

The Video Game Supply Company (VGS)is deciding whether to set production next year at 2,000,2,500,or 3,000 games.Demand could be low,medium,or high.Using historical data,VGS estimates the probabilities as 0.4 for low demand,0.3 for medium demand,and 0.3 for high demand.The following profit payoff table (in $100s)has been developed.

a.Determine the expected value of each alternative and indicate what should be the production target.
b.Determine the expected value with perfect information about the states of nature.
c.Determine the expected value of perfect information.

Question 58

Assume you are faced with the following decision alternatives and two states of nature.The payoff table is shown below.

Assume the states of nature have the following probabilities.

a.Determine the expected value of each alternative and indicate which decision alternative is the best.
b.Determine the expected value of perfect information.

Question 59

You are given the following payoff table.

Assume the following probability information is given.

a.Find the values of P(I₁)and P(I₂).
b.Determine the values of P(S₁|I₁),P(S₂|I₁),P(S₁|I₂),and P(S₂|I₂).
c.Use the decision tree approach and determine the optimal strategy.What is the expected value of your solution?

Question 60

Suppose we are interested in investing in one of three investment opportunities: d₁,d₂,or d₃.The following profit payoff table shows the profits (in thousands of dollars)under each of the 3 possible economic conditions-S₁,S₂,and S₃.The probability of the occurrence of S₁ is 0.1,and the probability of the occurrence of S₂ is 0.3.

a.Determine the expected value of each alternative and indicate which decision alternative is the best.
b.Determine the expected value with perfect information about the states of nature.
c.Determine the expected value of perfect information.

Question 61

You are given a decision situation with three possible states of nature S₁,S₂,and S₃.The prior probabilities of the three states are 0.20,0.45,and 0.35.With sample information I,you are provided with the following information.

a.Compute P(I).
b.Compute the revised probabilities of P(S₁|I),P(S₂|I),and P(S₃|I).

Question 62

Assume you have a sum of money available that you would like to invest in one of the two available investment plans: stocks or bonds.The conditional payoffs of each plan under two possible economic conditions are as follows.

a.If the probability of Economic Condition I occurring is 0.8,where should you invest your money? Use the expected monetary value criterion and show your complete work.
b.Compute the expected value with perfect information about the economic conditions (expected value under certainty).
c.Determine expected value of perfect information (EVPI).

Question 63

Consider the following profit payoff table.

What should the probabilities of S1 and S2 be so that the expected monetary values of the two decision alternatives equal one another?

Question 64

Assume you are faced with the following decision alternatives and two states of nature.The payoff table is shown below.

The probability of state of nature 1 is P(s₁)= 0.42.
a.Determine the expected value of each alternative.
b.Which decision is the optimal decision?
c.Determine the expected value with perfect information.
d.Compute the expected value of perfect information.

Question 65

A poll released this week found that in a random sample of registered voters,60% indicated that they think a female "will run" for the presidency,30% said a female "will not run," and 10% had "no opinion." When asked their opinions on whether or not a female would be elected,66% of those who said a female "will run" thought she could be elected;25% of those who thought a female "will not run" thought she could be elected;whereas,20% of those who had no opinion said that she could be elected.
a.What percentage of registered voters (in this sample)thought that a female could be elected?
b.Given that a person thought that a female could be elected,what is the probability that this person said a female "will not run" for the presidency?
c.Compute all the posterior probabilities.