The Monty Hall problem

Read this interesting math problem with a very counter-intuitive solution: For full details refer to wikipedia

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?

Because there is no way for the player to know which of the two unopened doors is the winning door, many people assume that each door has an equal probability and conclude that switching does not matter. However, as long as the host knows what is behind each door, always opens a door revealing a goat, and always makes the offer to switch, opening a losing door does not change the probability of 1/3 that the car is behind the player's initially chosen door. As there is only one other unopened door, the probability that this door conceals the car must be 2/3.