Don't Switch! Why Mathematicians' Answer to the Monty Hall Problem is Wrong

摘要

The Monty Hall problem is one of those rare curiosities -a mathematical problem that has made the front pages of national news. Everyone now knows, or thinks they know, the answer but a realistic look at the problem demonstrates that the standard mathematician's answer is wrong. The mathematics is fine, of course, but the assumptions are unrealistic in the context in which they are set. In fact, it is not clear that this problem can be appropriately addressed using the standard tools of probability theory and this raises questions about what we think probabilities are and the way we teach them.