When you first hear it, the Monty Hall Problem sounds simple enough. You're on the game show "Let's Make a Deal!" and host Monty Hall presents you with three doors. One, he says, has a car behind it. The other two are hiding live goats. He asks you to choose a door, and you go with Door #1. He then opens Door #3 to reveal ... a goat. He now gives you the chance to either stick with your choice of door, or switch to Door #2. Should you switch?
The seemingly obvious answer is that it doesn't matter — you've got a 50-50 shot at winning the car either way. The correct answer, however, is that you should absolutely switch.