Reverse balls and urn problem

Discussion in 'General Math' started by rveloso, Feb 28, 2010.

  1. rveloso

    rveloso Guest

    So here's a variant of the balls and urn problem im trying to solve.
    An urn has balls of 3 colors: black, white and red. Lets call the
    fraction of each color in the urn as P_b, P_r, P_w. Now, there's a
    process in which a user will randomly pick a ball from the urn and
    mark the color as seen, putting the ball back in the urn. The problem
    is the following, given that after a run of the experiment, only the
    color black was seen, what's the expected number of balls that were
    drawn from the urn? Obviously if at the end N colors were seen, the
    number of balls drawn is lower bounded by N i.e. n>=N, but i still
    could not get to the expectation of n...

    Any help appreciated, thanks!

    --Ricardo
     
    rveloso, Feb 28, 2010
    #1
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  2. rveloso

    Ken Pledger Guest


    Your question might get more expert attention in the
    <alt.sci.math.probability> or <sci.stat.math> news group.

    Ken Pledger.
     
    Ken Pledger, Mar 1, 2010
    #2
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  3. rveloso

    Peter Webb Guest

    Your problem cannot be solved (IMHO) because of how it is phrased. The
    expectation of n is meaningless in this question; you pick n and then
    undertake the experiment.

    A related question that is solvable is how many balls can you expect to pull
    out before you get one which isn't black. That is an easy combinatorial
    question, and I expect that this number minus 1 is what you are really
    after.
     
    Peter Webb, Mar 3, 2010
    #3
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