The Monty Hall Problem Explained in Just Over 5 Minutes

It’s a classic probability puzzle and regularly finds its way into mathematics lessons across the world.

The Monty Hall problem derived from a letter sent to the American Statistician by professor Steve Selvin in 1975, but became famous 15 years later. This is how it was posed in 1990, quoted in Marilyn vos Savant’s “Ask Marilyn” column in Parade magazine:

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?

The problem can vary depending on who tells it; sometimes there’s nothing behind the other two doors. But should you switch? If you think you should stick, think again. Adjunct professor Lisa Goldberg explains why being counterintuitive is your ticket to solving the Monty Hall problem. Spare yourself 6 minutes and grab a pen and paper if you need to. If you’d prefer an easier puzzle, why not try a nonogram?


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