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1. Consider a choice environment with two prizes, Z = {21,22}. in which the choice set comprises lotteries X over these two prizes, as in expected utility theory. Consider a compound lottery in which the prize is drawn as follows: 0 At the rst stage, a fair coin is ipped. If the coin comes up heads, a fair six-sided die is rolled and the prize is 21 if the number on the second die is 4 or below while it is 2:; if the number is 5 or 6. If the coin comes up tails, a fair coin is ipped again. In this case the prize is 21 if the second coin comes up heads, and 22 if it comes up tails. (a) Use a tree diagram as in class to illustrate the above compound lottery. (b) What is the single stage lottery to which the above compound lottery corresponds? (c) Suppose that prize 21 is strictly preferred to 22 and that assump- tions A2(a) and (b) (the substitution axioms) both hold. What can you say about the preferences as between the compound lot- tery in (a) and a. single stage lottery that offers prize 21 with probability 0.6 and 22 with probability 0.4