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A game involves tossing two coins. If the result is two heads, you win 3 points. If the result is one tail and one head, you win 1 point. If the result is two tails, you lose 5 points. Is this a fair game?

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  1. Outcomes:
    HH
    HT
    TH
    TT

    Prob(2 heads in 2 throws) = (1/2)(1/2) = 1/4
    prob(1 h, 1t) = 2/4 = 1/2
    prob(2 T) = 1/4

    expected value = (1/4)(3) + (1/2)(1) - 5(1/4) = 0

    yup, fair game, you can play it all night long

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