Consider buying a house whose fair 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.

a) What is the expected utility (i. e., expected net gain or loss in dollars) if you buy?

Someone is considering buying a house. But, the probability that currently it's in OK condition is estimated to be 75% which is P(ok) = 0.75. Now, you may hire someone to perform a home inspection before you buy. But, the inspection is not always accurate. Here are the probability:

- The inspection passes given that the house is actually OK is 80% -> P(pass | OK) = 0.8

- The inspection passes given that the house is not OK is 40% -> P(pass | ~OK) = 0.4

b) what is P(pass)?
c) what is P(OK | pass)?
d) what is P(OK | ~pass)?
e) If the inspection passes, and you want to buy, what is the expected utility?
f) If the inspection fails, and you want to buy, what is the expected utility?
g) How much, at most, should you pay for the home inspection?