TITLE: Probability of two people meeting in a given square grid.
QUESTION [19 upvotes]: Amy will walk south and east along the grid of streets shown. At the same time and at the same pace, Binh will walk north and west. The two people are walking in the same speed. What is the probability that they will meet?

I tried using Pascal's triangle but I have no idea how to proceed.

REPLY [3 votes]: Just a silly piece of code, approximating the answer...
#!/usr/bin/python3

from random import choice

A = [0, 0]
B = [5, 5]

N = 100000  # Number of simulations
n = 0       # Number of meetings
for _ in range(N) :
    a = A[:]
    b = B[:]
    while (b != A) & (a != B) & (a != b) :
        a[choice([i for (i, t) in enumerate(a) if (t != B[i])])] += 1
        b[choice([j for (j, t) in enumerate(b) if (t != A[j])])] -= 1
        n += (a == b)

print(n / N)