The Monty Hall problem is a brain teaser, in the form of a probability puzzle, loosely based on the American television game show Let’s Make a Deal and named after its original host, Monty Hall. The problem was originally posed in a letter by Steve Selvin to the American Statistician in 1975. It became famous as a question from a reader’s letter quoted in Marilyn vos Savant’s “Ask Marilyn” column in Parade magazine in 1990:

Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?

In search of a new car, the player picks a door, say 1. The game host then opens one of the other doors, say 3, to reveal a goat and offers to let the player pick door 2 instead of door 1.

Write a discussion post that assumes you’re on that game show in this situation.

1. What would your immediate instinct be in this situation? What action would you take?
2. Using the methods of calculating probability in this section, what do the results of the probability formulas tell you you should do?
3. This particular problem caused quite an uproar when it was published in vos Savant’s column. Why do you feel that people felt as strongly as they did, regardless of the answer they supported?

After you’ve posted, reply to at least two of your classmates. How do you feel your understanding of probability is strengthened by this discussion? Compare your answers to the ones others have shared. What do you feel that most people would do, if they were faced with this situation?