The Monty Hall Problem is a Numberphile video in which Lisa Goldberg, an adjunct professor in the Department of Statistics at UC, Berkeley explains why over the long-run contestants on Let's Make a Deal should have always switched doors. Numberphile published a short version and a long version of this video. The long version explains the mathematics behind the strategy that Goldberg suggests. Both videos are embedded below.
Applications for Education
As I watched these videos I thought about a couple of ways to use them in a mathematics lesson.
I would present the scenario to students and ask them for their ideas about whether or not a contestant should switch doors. Then I would show the video as part of the explanation to the problem.
Another way to use these videos is in conjunction with a hands-on lesson in which students survey schoolmates during lunch or after school. Your students could create a simple three choice game, eliminate one choice, then ask if the player wants to stick or switch. The data that students gather through this activity could be used by them to determine what they think is the best strategy. Show the video explanation after the data is collected and the students have shared their data-based strategies.