Two blind ants can only walk randomly upward or downward on a vertical rod. They are identical random walkers, with p being the probability of taking an upward step, and q = (1 - p) being the probability of taking a downward step. The step sizes of both ants are always the same. The two ants were initially at the same location. After each ant has taken N steps, what is the probability that they will again meet each other (i.e., they have reached the same location)?
Given that p = q = 1/2, plot a histogram of the probability against the number of steps.