Monty Hall Problem: This is based on the old television program Let’s Make a Deal, hosted by Monty Hall. There are three doors. Behind one of them is a grand prize, and nothing is behind the other two. You select a door. The host then opens one of the doors you didn’t select that has nothing behind it. You are offered the opportunity to switch your selection to the other unopened door. Should you switch or stick with your original selection?

This game can be simulated with playing cards. Use three cards, one of which is an ace, which represents the grand prize. Divide students into pairs. One student puts the three cards face down in front of the other student, who then guesses where the ace is. The first student, who knows where the ace is, turns up one of the cards that is not an ace. The other student can decide whether or not to switch.

Compute the proportion of times students win by switching and by not switching. Should you switch?