I have a combinatorics problem to solve, and I'm realy not sure how to do it. Here's the problem:
In [0,0] of a plane is a black piece and in [n,n] is a white one. The black moves each second per 1 to the right or up (equal probability). The white moves also each second per 1 to the left or down (equal probability). Determine the probability of their encounter.
First thing I started with was the conditions. They can't meet unless: n >= 0 and time is n seconds.
Next I tried to test the first few n: for n=0..3 the probability is {1, 2/4, 6/16, 14/100}, which didn't helped me much.
So how to approach this? I'd be much thankfull for any help..