The Car-and-Goats
A number of mathematicians were thrown into a tizzy by the following problem, which appeared in Marilyn vos Savant's column, "Ask Marilyn", in Parade(a Sunday newspaper supplement):

One of the three doors hides a car (all three equally likely) and other two hide goats. You choose Door 1. The host, who knows where the car is, then opens one of the other two doors to reveal a goat, and asks whether you wish to switch your choice. Say he opens Door 3, should you switch to Door 2?