Chapter 3 Decision Analysis Solution 3-31 to 3 - 45.pdf -...

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SOLUTIONS TO DISCUSSION QUESTIONS AND PROBLEMS 3-31. a. P(red) = 18/38; P(not red) = 20/38 b. EMV = Expected win = 10(18/38) + (-10)(20/38) = -0.526 c. P(red) = 18/37; P(not red) = 19/37 EMV = Expected win = 10(18/37) + (-10)(19/37) = -0.270 d. The enjoyment of playing the game and possibly winning adds utility to the game. A person would play this game because the expected utility of playing the game is positive even though the expected monetary value is negative. 3-32. A $10 bet on number 7 would pay 35($10) = 350 if the number 7 is the winner. P(number 7) = 1/38; P(not seven) = 37/38 EMV = Expected win = 350(1/38) + (-10)(37/38) = -0.526 3-33. Payoff table with cost of $50,000 in legal fees deducted if suit goes to court and $10,000 in legal fees if settle. Decision based on EMV: Go to court 3-34. EMV for node 1 = 0.5(100,000) + 0.5(40,000) = $30,000. Choose the highest EMV, therefore construct the clinic.
3-35. a b. EMV(node 2) = (0.82)($95,000) + (0.18)($45,000) = 77,900 8,100 = $69,800 EMV(node 3) = (0.11)($95,000) + (0.89)($45,000) = 10,450 $40,050 = $29,600 EMV(node 4) = $30,000 EMV(node 1) = (0.55)($69,800) + (0.45)($5,000) = 38,390 2,250 = $36,140 The EMV for using the survey = $36,140. EMV(no survey) = (0.5)($100,000) + (0.5)($40,000) = $30,000 The survey should be used. c. EVSI = ($36,140 + $5,000) $30,000 = $11,140. Thus, the physicians would pay up to $11,140 for the survey.
3-36 3-37. a. EMV(node 2) = (0.9)(55,000) + (0.1)($45,000) = 49,500 4,500 = $45,000 EMV(node 3) = (0.9)(25,000) + (0.1)(15,000) = 22,500 1,500 = $21,000 EMV(node 4) = (0.12)(55,000) + (0.88)(45,000) = 6,600 39,600 = $33,000 EMV(node 5) = (0.12)(25,000) + (0.88)(15,000) = 3,000 13,200 = $10,200 EMV(node 6) = (0.5)(60,000) + (0.5)(40,000) = 30,000 20,000 = $10,000 EMV(node 7) = (0.5)(30,000) + (0.5)(10,000) = 15,000 5,000 = $10,000 EMV(node 1) = (0.6)(45,000) + (0.4)(5,000) = 27,000 2,000 = $25,000

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