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Math Help - Probability mass function

  1. #1
    Super Member Anonymous1's Avatar
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    Probability mass function

    Suppose we draw three balls out of an urn that contains 15 balls numbered 1 to 15. Let X be the largest number drawn. Find the probability function of X.

    What I've got:
    For i>2, P(X=i) = \frac{(i-1)}{15}\times\frac{(i-2)}{14}\times\frac{1}{13}

    IDK just something feels wrong. Any help?

    Thanks
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  2. #2
    MHF Contributor matheagle's Avatar
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    I don't get that result.
    I would do it via chooses...

    P(X=15)={{1\choose 1}{14\choose 2}\over {15\choose 3}}

    and P(X=14)={{1\choose 0}{1\choose 1} {13\choose 2}\over {15\choose 3}}

    and P(X=13)={{2\choose 0}{1\choose 1} {12\choose 2}\over {15\choose 3}}

    and P(X=12)={{3\choose 0}{1\choose 1} {11\choose 2}\over {15\choose 3}}

    From this you can derive P(X=x), which is three times your answer

    P(X=x)={{15-x\choose 0}{1\choose 1} {x-1\choose 2}\over {15\choose 3}}

     ={3(x-1)(x-2)\over (15)(14)(13)}={(x-1)(x-2)\over (5)(14)(13)}
    Last edited by matheagle; January 31st 2010 at 08:49 PM.
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