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Math Help - Probability Questions

  1. #1
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    Nov 2009
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    Smile Probability Questions

    I really don't get this question and my work's due tomorrow any help is really appreciated!

    A game consists of rolling a dodeacahedral (12 faced) die and receiving the dollar amount equivalent to the roll. If the cost to play the game is $5 what is the expected payout for each round that is played?

    We're on discrete probability chapter, according to the back of my text book the answer should be $5

    I hope someone can help me, thanks in advance!!
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  2. #2
    Junior Member
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    Nov 2009
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    For discrete random variables, E(X) = \sum_{i=1}^{n}x_{i}P(X=x_{i})

    Therefore, if x_{i} = i \mbox{ for }i=1, 2, 3,...,12

    Then, E(X) = \sum_{i=1}^{12}x_{i}P(X=x_{i}) - 5 since you're paying 5 dollars to play.

    And P(X=x_{i}) = \frac{1}{12} \mbox{ for } i = 1, 2, 3,..., 12 since the die is a fair dodecahedron die.

    Thus, E(X) = [(1)\frac{1}{12} + (2)\frac{1}{12} + (3)\frac{1}{12} + ... + (12)\frac{1}{12}] - 5
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