|Speaker:||Dr. Jason Rosenhouse, James Madison University|
|Title:||The Monty Hall Problem Reconsidered|
The Monty Hall Problem is arguably the most famous and counterintuitive brainteaser in the history of mathematics. We are asked to imagine that while on a game show, we are presented with three doors. Behind one is a car, while the other two conceal goats. You select door number one, but before opening it Monty Hall, the host of the show, opens door two and shows you that there is a goat behind it. He now gives you the options either of sticking with door one, or switching to door three. The problem is to determine which choice gives you the better chance of winning the car. The interest in the problem stems from the fact that the answer that is obvious to most people, that with only two doors remaining there is only a 50-50 chance that either remaining door is correct, is entirely mistaken. By considering the classic Monty Hall Problem and a sequence of increasingly difficult variations on it, we shall come to understand how to think clearly about this and other probabilistic teasers. The talk will assume little in the way of mathematical background, and will mostly be accessible to all.