In my Statistics class we discussed the problem below and my knee jerk reaction was you have a 50/50 chance of winning whether you switch or stay. What do you think?
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?
Here’s a rather long and drawn out discussion about the whole problem on The Straight Dope, but he finally gets it right in the end.