A drunk man stands with a cliff one step to his left. He takes steps randomly left and right. Each step has probability p of going left and probability q=1−p of going right. Each step is the same size.
If allowed to randomly step indefinitely, what is the probability that the drunk falls off the cliff?
In purely mathematical terms, the drunkard starts at x=0 and steps +1 or −1 with each step. If he ever gets to x=−1 he falls off the cliff.