## Back to probabilities…

The following is taken from a textbook I have called The History of Mathematics: A Brief Course by Roger Cooke.  Note that I could not find an online reference to the actual mathematicians referred to in the problem so I have no idea what he’s referring to there.  It is nonetheless immaterial for the problem.

A famous example of mathematical blunders committed by mathematicians (not statisticians, however) occurred some two decades ago. At the time, a very popular television show in the United States was called Let’s Make a Deal. On that show, the contestant was often offered the chance to keep his or her current winnings, or to trade them for a chance to win some unknown prize. In the case in question the contestant had chosen one of three boxes, knowing that only one of them contained a prize of any value, but not the contents of any of them. For ease of exposition, let us call the boxes, A, B, and C, and assume that the contestant chose box A.

This problem provides an interesting way to continue the discussion started over on The Pontiff’s blog.