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Random Walk - Falling into a pool

  1. Sep 28, 2010 #1
    1. The problem statement, all variables and given/known data

    A clown stands at the side of a swimming pool. In his hand is a bag containing [tex]n[/tex] red balls and [tex]n[/tex] blue balls. At each step he puts his hand into the bag and pulls out a random ball and throws it away. If the ball is red, he makes a step towards the pool and if it is blue, he makes a step away from the pool. What is the probability that the clown falls in to the pool?

    3. The attempt at a solution

    Let R be the probability that he draws a red ball. Let B be the probability he draws a blue ball.

    P(falling) = R + B[tex]\left[ RR + RB... \right][/tex]

    I want to do some kind of recursion but I'm not exactly sure if I'm approaching this problem correctly.

    Any help?
  2. jcsd
  3. Sep 28, 2010 #2
    Draw a tree diagram and look at the probability that you fall into the pool the first step, the second step etc. Try find a formula and sum all these probabilities.
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