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Math Help - Card Problem

  1. #1
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    Card Problem

    In a particular game of chance, a 3-card hand is dealt to the player from a standard deck of 52 cards. The player wins $20 for each diamond in their hand. If the game is fair, how much should the player have to pay to play this game?
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  2. #2
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    Quote Originally Posted by zackgilbey View Post
    In a particular game of chance, a 3-card hand is dealt to the player from a standard deck of 52 cards. The player wins $20 for each diamond in their hand. If the game is fair, how much should the player have to pay to play this game?
    Start by defining a random variable. Let X be the random variable number of diamonds in the hand.

    Calculate Pr(X = 0), Pr(X = 1), Pr(X = 2) and Pr(X = 3).

    Let Y be the random variable amount of money ($) player wins.

    State the value of Pr(Y = 0), Pr(Y = 20), Pr(Y = 40) and Pr(Y = 60).

    Let m be the amount of money ($) paid to play the game.

    For a fair game, E(Y) = m. Therefore:

    m = Pr(Y = 0) (0) + Pr(Y = 20) (20) + Pr(Y = 40) )40 + Pr(Y = 60) (60) = ....
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    that makes it easier, but what do they mean by 'fair'?
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  4. #4
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    Quote Originally Posted by zackgilbey View Post
    that makes it easier, but what do they mean by 'fair'?
    Fair means that the E(amount won) = amount paid to play, that is, E(Y) = m, that is, E(profit) = 0.
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