Probability and random walk

1. Sep 6, 2006

mathlete

The question:

"Two men start out together at the origin, each having a 1/2 chance of making a step to the left or right along the x-axis. Find the probability that they meet again after N steps."

It then says it may help to consider their relative position but I don't see how that would help.

The probability for one person is Wn(n1) = N!/[(n1!)(N-n1)!]*p^n1*q^(N-n1)

where N is total steps, n1 is steps to the right, p = q = 1/2 (for this problem). I just don't know how to combine/adjust it for two people.

Also, i'm not sure, but would this involve an integral from 0 to N steps at some point (to cover all cases)?

2. Sep 6, 2006