Consider a DM in the expected utility framework. a. Suppose the DM prefers lottery A to lottery B. Now take any probability p and any third lottery C. State what the Independence Axiom requires for this DM.

Take A = {50% of 0, 50% of 100} and B = {100% of 40}. Assume the DM prefers A to B. Now take lottery C = {40% of 0, 50% of 100, 10% of 200} and lottery D = {80% of 40, 10% of 100, 10% of 200}. b. Find a lottery E and a probability p so that you can (i) write lottery C as a mixture of A and E, of the form C = {p of lottery A, 1-p of lottery E}, and (ii) write lottery D as a mixture of B and E of the form D = {p of lottery B, 1-p of lottery E}. c. Assuming (only) that the DM obeys EU theory (and still prefers A to B), does she prefer C to D, D to C, or can it not be determined? Provide a one sentence explanation.