Random Walk - Falling into a pool

[noblerare]

Homework Statement

A clown stands at the side of a swimming pool. In his hand is a bag containing n red balls and n 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 into the pool?

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\left[ RR + RB... \right]

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

Any help?

 

[Inferior89]

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.