Suppose that your utility function is 11(x) = ./x, and that you are offered a gamble which allows you to win $4 if you are lucky and $1 if you are not.

(a) Suppose, first, that the probability of winning $4 is 1/4 and the probability of winning $1 is 3/4. What is the expected value of this gamble?

(b) Suppose, that the probability of winning$! is still 1/ -1 and the probability of winning Sl is 3/-t What is the expected utility of this gamble?

(c) Suppose, that the probability of winning $-1 is stiJI 1/ -1 and the probability of winning $1 is 3/-1. What is the certainty equivalent of the gamble, that is, what is the amount of money X such that you are indifferent between receiving $X for sure and playing the gamble?

(d) Imagine now that the probability of winning 5-! is p and the probability of winning $1 is (1- p). If the utility of the gc1mble equals 3/2, what 1s p?