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    Probability : Dice and Payoff

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    Suppose you roll two dice
    a) What are the odds in favor of rolling a sum of 10?
    b) What are the odds against rolling a sum of 7 or 11?
    c) In part a, if you bet one dollar that a sum of 10 will turn up, what should the house pay (plus returning your one dollar bet) if a sum of 10 turns up for the game to be fair?

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    Solution Preview

    a) Let x=number of points on the first die and
    y=number of points on the second die.

    Then P(x+y=10)=3/36=1/12
    since we have 3 wining possibilities for x+y=10 ...

    Solution Summary

    Probabilities of dice rolls are determined, as well as payoff information if one was gambling on an outcome.