Suppose that a person must accept a gamble X of the following form:
Pr(X = a) = p and Pr(X = 1− a) = 1− p, where p is a given number such that 0 < p < 1. Suppose also that the person can choose and fix the value of a (0 ≤ a ≤ 1) to be used in this gamble. Determine the value of a that the person would choose if his utility function was U(x) = log x for x >0.