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1 The expected value of perfect information places an upper bound as to what one might be willing to pay for additional information to aid in making a decision. a. True b. False 2 You have the following expectations based on your analysis of a process. You believe that there is a 50% chance of being moderately effective and a 20% chance of being highly effective: You are trying to decide whether to do testing before making a decision. Ineffective Moderately Effective Highly Effective Expected Value Proceed with testing
Decide not to test
Calculate the expected values to proceed with testing and to decide not to test, respectively. a. 250, 0 b. 250, 100 c. 650, 0 d. 800, 0 e. 800, 100 Ineffective Moderately Effective Highly Effective Expected Value Proceed with testing
Decide not to test 0 0 0
3 When calculating the expected value of perfect information, “perfect information” refers to knowing in advance when each of the possible states of nature will occur. a. True b. False 4 Utilization of Bayes' Theorem permits decision-makers to work with revised probabilities, which are known as: a. prior probabilities b. marginal probabilities
c. utility numbers d. expected monetary values (EMV) e. posterior probabilities 5 A market research survey is available for $10,000. Using a decision tree analysis, it is found that the expected monetary value with the survey is $65,000. The expected monetary value with no survey is $62,000. Based on this information, the survey should be taken. a. True b. False The survey is worth $65,000 - $62,000 = $ 6 Before a marketing research study was done, John Colorado believed there was a 50/50 chance that his music store would be a success. The research team determined that there is a 0.9 probability that the marketing research will be favorable given a successful music store. There is also a 0.8 probability that the marketing research will not be favorable given an unsuccessful music store. If the marketing research is favorable, what is the revised probability of a successful music store? a. 0. b. 0. c. 0. d. 0. e. 0.
[S=Successful, U=Unsuccessful, F=Favorable, N=Not Favorable; P(S)=.50,
P(U)=.50; P(F/S)=.90, therefore P(N/S)=.10; P(N/U)=.80, therefore, P(F/U)=.20;
Using Bayes’ Theorem, P(A|B) = P(B|A)P(A)/[P(B|A 1 )P(A 1 ) + P(B|A 2 )*P(A 2 )]:
P(S|F) = P(F|S)P(S)/[P(F|S)P(S) + P(F|U)*P(U)]=(.90)(.50)/[(.9)(.50)+(.20)(.50)]
Or, using a Joint Probability Table to calculate P(S/F).]
Joint
Probability
Table
Successful Unsuccessful Probability
Favorable
P(F&S)=
P(FIS)*P(S)=
P(F&U)=
P(F/U)*P(U)=
P(F)=.
Not
Favorable
P(N&S)=
P(N/S)*P(S)=
P(N&U)=
P(N/U)*P(U)=
P(N)=.
Probability P(S)=0.50 P(U)=0.50 1.
12 The Expected Value with Perfect Information (EVwPI) can be determined without using probabilities. a. True b. False 13 Bayes’ Theorem can be used to combine prior probabilities of events with market research results. a. True b. False 14 Salvage value is realized when the production quantity exceeds the demand. a. True b. False 15 When solving a decision tree, expected values are computed at decision nodes. a. True b.False 16 If EVSI = 100, EVBest = 1000 (this is the best decision), and EVc = 1200 (this is the best possible return, which would be used to calculate EVPI), then Efficiency = a. 0. b. 1 c. 50 d. 100 e. 150 =100/(1200-1000) 17 Selling price per unit is $45; Variable cost per unit is $5; Salvage value per unit is $2 (this is the per piece value of undemanded products); Cost of lost sales is $1. Find the profit when 60 units are produced and the state of nature is a demand of 40 units. Do not include fixed costs. a. = 4540 - 540 - 1* b. = 4540 - 560 + 2* c.** = 4560 - 540 - 1* d. = 4540 - 560 + 220 - 1 e. = 4560 - 540 + 220 - 1 18 Using the following joint probability table, find P(A1/B2): B1 B2 P(A) A1 .10 .20.
A2 .40 .30.
P(B) .50 .50 1.
a. .10 b. .30 c. .33 d. .40 e.. 19 Consider the following payoff (profit) table. Which decision would be selected by a person using Maximin as a criteria? Decision States of Nature 1 2 3 4 5 A 20 40 60 80 100 B 2 92 2 2 2 C -50 92 94 96 98 a. A b. B c. C d. A and B e. B and C 20 In the previous payoff (profit) table above, what is the EVc given the following probabilities? P(1) = .1; P(2) = .2; P(3) = .5; P(4) = .1; P(5) = .1, a. .12 + .240 + .52 + .12 + .1* b. .12 + .292 + .52 + .12 + .1* c. .1(-50) + .292 + .594 + .196 + .1* d. .120 + .240 + .560 + .180 + .1* e. .120 + .292 + .594 + .196 + .1***
