2. Preferences under uncertainty Suppose Felix is offered the opportunity to take part in one of two gambles. Gamble A pays $100 with probability 0.92, $500 with probability 0.04, and nothing with probability 0.04. Gamble B pays $100 with certainty. Which of the following inequalities reflects a preference for gamble B over gamble A if Felix's utility from earning X dollars is given by U(X)? ○ U(100) > U(0.92 × 100) + U(0.04 × 500) + U(0.04 × 0) OU(100) U(0.92 x 100) + U(0.04 x 500) + U(0.04 x 0) ⒸU(100)>0.92U(100) +-0.04U (500) +0.04U(0) OU(100) <0.92U (100) +0.04U (500) + 0.047(0) Now suppose he is offered a second set of gambles. Gamble C pays $100 with probability 0.44, $500 with probability 0,04, and nothing with probability 0.52. Gamble D pays $100 with probability 0.52 and nothing with probability 0.48. If Felix's preferences are consistent, he should prefer gamble
2. Preferences under uncertainty Suppose Felix is offered the opportunity to take part in one of two gambles. Gamble A pays $100 with probability 0.92, $500 with probability 0.04, and nothing with probability 0.04. Gamble B pays $100 with certainty. Which of the following inequalities reflects a preference for gamble B over gamble A if Felix's utility from earning X dollars is given by U(X)? ○ U(100) > U(0.92 × 100) + U(0.04 × 500) + U(0.04 × 0) OU(100) U(0.92 x 100) + U(0.04 x 500) + U(0.04 x 0) ⒸU(100)>0.92U(100) +-0.04U (500) +0.04U(0) OU(100) <0.92U (100) +0.04U (500) + 0.047(0) Now suppose he is offered a second set of gambles. Gamble C pays $100 with probability 0.44, $500 with probability 0,04, and nothing with probability 0.52. Gamble D pays $100 with probability 0.52 and nothing with probability 0.48. If Felix's preferences are consistent, he should prefer gamble
Chapter7: Matrices And Determinants
Section7.2: Operations With Matrices
Problem 12ECP
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