Suppose is a preference over lotteries of two prizes z1,z2 that satis- fies the A2 axiom (substitution). Suppose we are given that z1 z2. Show that the lottery [(z1; 0.9), (z2, 0.1)] is strictly preferred to the lot- tery [(z1; 0.7), (z2, 0.3)] by breaking the lotteries into compound lotter- ies with a common lottery on the left branch and different pure prizes on the right branch tree diagram