Monty Hall Problem : Solution

Introduction

The Three Doors Problem, or Monty Hall Problem, is familiar to statisticians as a paradox in elementary probability theory often found in elementary probability texts (especially in their exercises sections). In that context it is usually meant to be solved by careful (and elementary) application of Bayes’ theorem. However, in different forms, it is much discussed and argued about and written about by psychologists, game-theorists and mathematical economists, educationalists, journalists, lay persons, blog-writers, wikipedia editors.

In this article I will briefly survey the history of the problem and some of the approaches to it which have been proposed. My take-home message to you, dear reader, is that one should distinguish two levels to the problem.

There is an informally stated problem which you could pose to a friend at a party; and there are many concrete versions or realizationsof the problem, which are actually the result of mathematical or probabilistic or...