b) Since Jill's preferences violate the independence axiom, we know that they do not admit an expected utility representation. Show directly that it is impossible to assign utilities to the outcomes so that the ranking of the expected utilities of the three lotteries matches Jill's preference ranking. [Hint: To do this, rst assume that the outcomes generate utilities . Then compute the expected utilities of the three lotteries above, and derive a contradiction between the inequalities corresponding to Jill's prefere nces.]