1. (20 pts) If you were offered a choice between bets A and B, which one would you choose? Bet A You win $1,000,000 for sure Bet B You win $5,000,000 with probability 0.10 You win $1,000,000 with probability 0.89 You win $0 with probability 0.01 Now choose between bets C and D: Bet C You win $1,000,000 with probability 0.11 You win $0 with probability 0.89 Bet D You win $5,000,000 with probability 0.10 You win $0 with probability 0.90 Assume that the expected utility hypothesis holds. (1) Prove that if you chose bet A, you should have also chosen bet C. (2) Prove that if you chose bet B, you should have also chosen bet D. Note: Empirical observations violating the results in (1) or (2) have been called Allais' paradox