Consider four gambles X1, X2, X3, and X4, for which the probability distributions of the gains are as follows:
Pr(X1 = 0) = 0.2, Pr(X1 = 1) = 0.5, Pr(X1 = 2) = 0.3;
Pr(X2 = 0) = 0.4, Pr(X2 = 1) = 0.2, Pr(X2 = 2) = 0.4;
Pr(X3 = 0) = 0.3, Pr(X3 = 1) = 0.3, Pr(X3 = 2) = 0.4;
Pr(X4 = 0) = Pr(X4 = 2) = 0.5.
Suppose that a person’s utility function is such that she prefersX1 toX2. If the person were forced to accept either X3 or X4, which one would she choose?