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Math Help - roulette number repeat...two workings dif answers..1wrong-why?

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    Member ssadi's Avatar
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    Cool roulette number repeat...two workings dif answers..1wrong-why?

    Hi,
    Suppose a roulette (with 38 numbers) is spun 12 times, and the probability of any number repeated is required.

    So:
    Working 1: 38C1*12C2*(1/38)^2*(37/38)^10.......gives a value greater than 1 so obviously wrong. (success occuring twice for a single number, then accounting for 38 separate no.s)
    Working 2: No repeat= 38*37*36*..*27/(38)^12. So at least one repeat=1-no repeat=1-.143=.857 probability...looks better, and sufficient for my task.

    Problem is...how do I find out the probability of any number occuring thrice exactly, or at least probability of any number occuring twice exactly, as the working 1 doesn't work, and working 2 is only applicable for the special case and no more Why just when I think I have learnt something about probability it eludes me.

    Heeeelp!
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    Re: roulette number repeat...two workings dif answers..1wrong-why?

    Quote Originally Posted by ssadi View Post
    Hi,
    Suppose a roulette (with 38 numbers) is spun 12 times, and the probability of any number repeated is required.

    There are \mathcal{T}=\binom{12+38-1}{12} total of outcomes.

    There are \mathcal{D}=\binom{38}{12} ways to have all different outcomes.

    The probability of all different outcomes is \frac{\mathcal{D}}{\mathcal{T}}.

    So the probability of at least one repeated outcome is 1-\frac{\mathcal{D}}{\mathcal{T}}.

    Now I am not sure that is actually what you mean by "any number repeated".
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  3. #3
    Member ssadi's Avatar
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    Re: roulette number repeat...two workings dif answers..1wrong-why?

    no, I don't think I meant what you think I meant
    You are saying the probability of a particular set of number of appearing
    I am saying that say..2 appears at least twice, or 15 appears exactly 3 times... in the 12 trials
    How to get that probability?
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    Re: roulette number repeat...two workings dif answers..1wrong-why?

    Quote Originally Posted by ssadi View Post
    no, I don't think I meant what you think I meant
    You are saying the probability of a particular set of number of appearing
    I am saying that say..2 appears at least twice, or 15 appears exactly 3 times... in the 12 trials
    How to get that probability?
    In that case, you need to give a full and complete detailed description of the setup.

    When you use the word any it does not mean a particular set.
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  5. #5
    Member ssadi's Avatar
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    Re: roulette number repeat...two workings dif answers..1wrong-why?

    for example
    12 trials

    any number in the set (00,0...36) repeats itself

    within the 12 trials

    I don't know how i can be more specific

    similarly, say

    any number in the set (00, 0...36) appears exactly 3 times in the 12 trials
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