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Math Help - probability of winning after 50 rounds

  1. #1
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    probability of winning after 50 rounds

    A die is rolled and you are paid $9 when it shows 6 dots, but you have to
    pay $5 when it shows 1 or 2 dots. You play 50 rounds of this game. What
    is the probability of winning (overall) some money.

    a hint was given: construct the probability generating function of your total net win

    but im having a hard time getting anywhere at all
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  2. #2
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    Quote Originally Posted by chrisc View Post
    A die is rolled and you are paid $9 when it shows 6 dots, but you have to
    pay $5 when it shows 1 or 2 dots. You play 50 rounds of this game. What
    is the probability of winning (overall) some money.

    a hint was given: construct the probability generating function of your total net win

    but im having a hard time getting anywhere at all
    Here's a start:

    Let X be the random variable winnings in a single game.

    Pr(X = -5) = 2/6, Pr(X = 0) = 1/2, Pr(X = 9) = 1/6.

    Define Y = X_1 + X_2 + \, .... + X_{50} where the X_i are i.i.d. random variables with distribution given above.

    You need to calculate Pr(Y > 0).
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  3. #3
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    ah good, im going to give this a try and ill report back
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