TV Puzzle

Imagine you're on a game show on tv, and you're offered the choice of three prizes behind closed doors. One of the prizes is very valuable (usually a car), and behind the other two doors are worthless prizes (often goats). You don't know what's behind which door, but the game show host does. You choose a door (hoping to get the car). The host, instead of opening your selected door, raises the tension by opening one of the other two doors instead, behind which he knows there is a goat. Then he offers you the choice - do you stick with your previously-selected door, or do you switch to the other, still closed, door?

Solution:
You raise your chances of getting the car by switching. The chance of the car being behind your original choice is 1 in 3. Now that one of the other two doors has been removed, the chance that the car is behind the other closed door is now 2 in 3, which is over twice as likely. It's extremely counter-intuitive because it's common to think that the chances are now 50:50, but they're not. Another way to look at this: if you chose a goat, you should switch, and if you chose the car, you should stick. But in the first round, you probably chose a goat (which was twice as likely as choosing the car). So you will probably gain by switching doors, and probably lose by sticking with your original choice.