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1. A DoD contractor is attempting to decide whether to purchase a new drill press, a lathe, or a grinder. The return from each will be determined by whether the company succeeds in getting a government military contract. The profit or less from each purchase and the probabilitles associated with each contract outcome are shown in the following payoff table: Contract No Contract Purchase .60 .40 Drill press S40,000 5-8,000 Lathe 20,000 4,000 Grinder 12.000 10,000 The machine shop owner is considering hiring a military consultant to ascertain whether the shop will get the government contract. The consultant is a former military officer who uses various personal contacts to find out such information. By talling to other shop owners who have hired the consultant, the owner has estimated a 70 probability (P(F|) -0.70) that the consultant would present a favorable report, given that the contract is awarded to the shop(true positive), and a 80 probability (P(Un) = 0.80) that the consultant would present an unfavorable report, given that the contract is not awarded (True Negative). Using decision tree analysis, determine the decision strategy the owner should follow the expected value of this strategy, and the maximum fee the owner should pay the consultant Use Bayes Theorem to calculate all the probabilities required to solve this decision tree problem. Full credit will only be given if the actual calculations are shown. Partial credit for correct answers or correct use of formulas will be given. Please show all work. From the payoff table: P(C) is the probability that contract is awarded, P(C) = 0.60 P(n) is the probability of no contract awarded, P(n) = 0.40 Prior information: PCF|C) is the probability that the consultant would present a Favorable report, given that the contract is awarded to the shop, P(Fl) = 0.70 P(Uln) is the probability that the consultant would present an Unfavorable report, given that the contract is Not awarded, P(U In) = 0.80 What are P(F|n) and P(UIC), le the probabilities that the analyst will NOT predict contract or no-con-tract correctly. P(UIC) = __ and PCF|n) = ? (Hint: here no long calculation needed) Solution. Using Bayes Theorem Pe F-PCF)=P(Fe)-P(e) we express: Pel F) = P(Fic)P(C) P(FIC)-P(C) P(FIC) PC) 0.7*0.6 P(F) P(5.c) + P(En) P(FIC)-P()+ P(Fin).P(n) 0.7*0.6 + ... Find probabilities and answer questions 1 -4. P(F) = Pelu) P(nu) P[F) = PU) = 1. With these probabilities, create and draw a decision tree for this problem. Follow discussion and example we went over in class on Thursday. 2. Should the owner of the shop hire the military consultant? [le. the value of consultant's expertise worth $17.500) 3. What is the maximum amount that the owner would be willing to pay to the consultant for the expert advice? 4. What is the efficiency of the sample information