Question

# 5 (5) (15 points) Consider a simplified roulette with 3 numbers where the player is not...

5

(5) (15 points) Consider a simplified roulette with 3 numbers where the player is not betting on a specific number at each turn of the wheel but is winning or losing a fixed amount of money depending on which of the 3 numbers occurs. The roulette can be switched between two states A and B. The operator of the wheel is likely to select state A with probability 0.7 and state B with probability 0.3. When in state A the probability of getting each of the 3 numbers is P({1})=0.3, P({2)) = 0.5 and P({3}) = 0.2 respectively. When in state B these probabilities are P({1}) = 0.4, P({2})=0.4 and PC{3}) = 0.2. In addition, suppose that the amount of money you win depends on the state of the wheel. When in state A you win 18 if 1 or 3 occur and you lose 1\$ if 2 occurs. When in state B you win 1\$ if 2 or 3 occur and you lose 1\$ if 1 occurs. Suppose that to play this game you need to pay 0.28. Compute the expected win to decide whether you want to play the game or not.

Si, As a Whole 0.2-0.06 = 0.14 \$ I am in lose

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