Sample Question #289 (stochastics)
A drunkard is at the 17th meter of a 100-meter-long bridge. He has a 50% chance of staggering forward or backward one meter each step. What is the probability that he will make it to the end of the bridge (i.e., the 100th meter) before the beginning (the 0th meter)? What is the expected number of steps he takes to reach either the beginning or the end of the bridge?
[Taken from Chapter 5 of Zhou, A Practical Guide to Quantitative Finance Interviews]