Chapter 4.7, Problem 226E

Monty Hall Problem. Several years ago, in a column published by Marilyn vos Savant in Parade Magazine, an interesting probability problem was posed. That problem is nowreferred to as the Monty Hall Problem because of its origins from the television show Let’s Make a Deal. Following is a version of the Monty Hall Problem. On a game show, there are three doors, behind each of which is one prize. Two of the prizes are worthless and one is valuable. A contestant selects one of the doors, following which, the game-show host—who knows where the valuable prize lies—opens one of the remaining two doors to reveal a worthless prize. The host then offers the contestant the opportunity to change his or her selection. Should the contestant switch? Verify your answer.