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Homework Help: Infinite supply of marbles probability problem

  1. Sep 3, 2010 #1
    1. The problem statement, all variables and given/known data
    A has an infinite supply of marbles numbered 1,2,3,... A places the marbles, two at a time and in numerical order, into an urn (i.e. first 1 and 2, then 3 and 4, etc.). Each time A puts two marbles, B reaches in and pulls on out. This process goes on forever.

    c) If B always removes marbles randomly (each marble in the urn equally likely to e removed), with what probability will marble number 1 remain in the urn forever?


    2. Relevant equations



    3. The attempt at a solution
    Here is what I did:
    1,2 =>prob that 1 stays is 1/2

    1,3,4 => prob that 1 stays is 2/3

    1,3,4,6 =>prob that 1 stays is 3/4

    until (n-1)/n

    so we need to multiply them all and we are left with 1/n
    so as n->inf, the probability that it happens is zero ?

    Is my answer correct ?

    Thanks,
    Roni.
     
  2. jcsd
  3. Sep 3, 2010 #2

    Dick

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    Science Advisor
    Homework Helper

    Re: Probability

    Seems fine to me.
     
  4. Sep 3, 2010 #3
    Re: Probability

    I see, thanks very much :)
     
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