Three Doors, One Prize

A game show offers three doors. Behind one sits a car; behind the other two, goats. You pick door 1. The host, who knows where the car is, opens door 3 to show a goat. Then he asks: switch to door 2, or stay?

Most people shrug and say it cannot matter now. They are wrong. Switching wins two-thirds of the time. Your first pick had a 1/3 chance, so there was a 2/3 chance the car was elsewhere. The host's reveal pours that whole 2/3 onto door 2.