Aka - A Totally Confusing Problem that Shows how Difficult it is to Conquer Intuition
You visit your grandma in Los Angeles, and she insists upon taking you to a game show that she enjoys watching on television. By a strange course of fate, you end up on stage as a contestant. The host of the show tells you that behind one of the three doors in front of you lies a brand new Cadillac Escalade. Behind two of the other doors is a booby prize.
He asks you to make your choice. You choose door number one. "Contestant chooses door number one!" announces the host. One of the hostesses walks over to stand between door number one, and door number 2. "Sherry, lets show our contestant what's behind door number TWO!" says the host. The hostess opens door number two, which contains a booby prize (in this situation, we assume that the show always opens another door that contains a booby prize when the contestant makes his selection).
The host tells you you have a chance to think about your decision, and pick door number three if you want. What do you do?