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1. Two random walkers start out together at the origin, each having equal probability of making a step to the left or right along the r axis. Find the probability that they meet after N steps. (They take their steps simultaneously. It may be helpful to consider their relative motion.)
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Answer #1

Here as motion is considered to be relative, total steps will be 2N.

Therefore,

probability is

P = N! / (N + m / 2 ) ! 2N

here N = 2N and m = 0

P = 2N / (2N N!)2

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