Question

Consider a simplified roulette with 3 numbers where the playeris not betting on a specific number at each turn of the wheel but is winningor losing a fixed amount of money depending on which of the 3 numbersoccurs. The roulette can be switched between two statesAandB. Theoperator of the wheel is likely to select stateAwith probability 0.7 and stateBwith probability 0.3. When in stateAthe probability of getting each ofthe 3 numbers isP({1}) = 0.3,P({2}) = 0.5 andP({3}) = 0.2 respectively.When in stateBthese probabilities areP({1}) = 0.4,P({2}) = 0.4 andP({3}) = 0.2. In addition, suppose that the amount of money you windepends on the state of the wheel. When in stateAyou win 1$ if 1 or 3occur and you lose 1$ if 2 occurs. When in stateByou win 1$ if 2 or 3occur and you lose 1$ if 1 occurs. Suppose that to play this game you needto pay 0.2$. Compute the expected win to decide whether you want to playthe game or not.

Answer 1

ANSWER::

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

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