21: Monty Hall problem

An interesting problem raised in movie 21:

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 answer is somewhat counter intuitive: switch gives a 67% chance of winning while stay with original only has 33%. The way to best understand this is to give up your intuition, use the more fundentmental "decision tree" to evaluate the probabilities: (picture linked from wikipedia):

Another interesting probability topic of the movie is card counting in BlackJack...