3. Suppose an individual makes two choices over two sets of lotteries. First, the individual chooses between A and A*, then the individual makes a second choice between B and B*. These lotteries have outcomes and probabilities given by: A 6 Choice 1 Vs. 1/2 A* 6 Choice 2 B Vs. B* 6 1/4 6 2/3 1/3 0 2 1/2 1/3 0 2 2 213 0 0 0 3/4 0 (a) Let x = 0, x2 = 2, and x3 = 6. Sketch a graph of the probability triangle with P3 on the vertical axis and p on the horizontal axis. Plot and label each of these 4 individual lotteries. (b) Suppose that an individual strictly prefers A over A* and strictly prefers B over B*. Sketch indifference curves in your graph that are consistent with these pref- erences. (c) Is this individual risk averse, risk neutral, or risk inclined? How do you know? (d) Now suppose that a different individual strictly prefers A* over A and strictly prefers B_over_ B*. Show that expected utility theory is inconsistent with this individual's preferences