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Math Help - prob dice question

  1. #1
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    prob dice question

    you throw 1 dice until you get K times the number '6'
    X = the number of your throws.
    what is P(X) ?
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  2. #2
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    The probability that N throws contains (K-1) '6's somewhere in the first (N-1) throws, with a '6' on the N-th throw is \binom{N-1}{K-1} \left(\frac56\right)^{(N-1)-(K-1)} \left(\frac16\right)^{K-1} \frac16.
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  3. #3
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    how can i prove that ∑ p(X)=1 ?
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  4. #4
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    Quote Originally Posted by amitbern
    how can i prove that ∑ p(X)=1 ?
    I'm not quite sure what you want to prove here. This sum has to be 1
    since with probability 1 you will eventually reach K sixes. So the sum
    of the probabilities of the number of throws needed for this is 1.

    RonL
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  5. #5
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    I know that it's supposed to be 1,
    but how can i prove it mathematically (Newton’s binomial )?
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