Question

Part IV. Decision Theory (40 points) Consider buying a house whose market value is $500K, but you can get it for $450K. However, there is a risk: if the house has structural problems (its current condition is not OK), you will have to spend $110K to fix it. The probability that currently it's in OK condition is estimated to be 75%; that is, P(OK) : 0.75. 1) (4 points) What is the expected utility (i.e., expected net gain or loss in dollars) if you buy? 2) (4 points) You may hire someone to perform an inspection before you decide to buy. However, the inspection is not always accurate. You estimate that the probability that . the inspection passes given that the house is actually OK is 80%; that is, Ppass/OK):080; . the inspection passes given that the house is not OK is 40%; that is, POass/-OK)-0.40. What is Pípass) - the overall probability that the house passes the inspection? 3) (4 points) Compute P(OK/pass) 4) (4 points) Compute P(OK/-pass)- 5) (8 points) If the inspection passes, and you want to buy, what is the expected utility? 6) (8 points) If the inspection fails, and you want to buy, what is the expected utility? 7) (8 points) Should you pay for the inspection? If so, at most how much should you pay the inspector?

Answer 1

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