Interview Question: Drunken Man

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]

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One Response to Interview Question: Drunken Man

  1. Brett says:

    ANSWER
     
    The answer is (1) 0.17, and (2) 1441. There’re several ways to solve this problem. The simplest is via a martingale argument;
    for details, please see pp. 116-117 of A Practical Guide to Quantitative Finance Interviews.

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