Consider a utility function U for which U(0) = 5, U(1) = 8, and U(2) = 10. Suppose that a person who has this utility function is indifferent to either of two gambles X and Y, for which the probability distributions of the gains are as follows:
Pr(X =−1) = 0.6, Pr(X = 0) = 0.2, Pr(X = 2) = 0.2;
Pr(Y = 0) = 0.9, Pr(Y = 1) = 0.1.
What is the value of U(−1)?