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Math Help - Red and Black balls in urn

  1. #1
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    Sep 2009
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    Red and Black balls in urn

    An urn contains n+m balls, n red and m black
    let X be the number of red balls chosen without replacement before a black one is chosen. We are intressted in E(x). To obtain this quantity, number red balls from 1 to n and define Xi, i=1,...,n by
    Xi{ 1 of red ball i is chosen ,
    0 otherwise

    so i get what's going on....firstly, the probability of drawing a red ball is n/n+m...and i need to show that the answer is the mean of a geometric dist: 1/p.

    So i need to write E(x)= summation of i from 1 to n (xi)
    but i don't know how to proceed... something like sum(xi* P(xi))... i dont really know how to insert the notation either
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  2. #2
    Super Member
    Joined
    Apr 2009
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    Thanks
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    I got the following recursive expression for your problem

    E(x) which I prefer to write as E(n,m) as it is a function of n,m

    E(n,m) = n/(n+m) E(n-1,m) + 1

    Note the end condition E(0,m) = 1

    To check your answer you can use E(n,0) = n

    Hope it helps !
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