This is a puzzle I picked up from the Movie “21” that I was watching 2 days back. The scene is a class in MIT, where the professor gives this problem to one of the students. Here it goes:
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?Please send your answers directly to me on e-mail – alokgoyal_2001@yahoo.com
Alok Goyal's Puzzles Page 
Well this is very counter-intuitive (and all good puzzles are). Instead of explaining it in probability, I would just put in a grid of options available (3 in this case, assuming 2 goats are identical :-)). When you put that through, you realize that switching the door improves the odds.
Have seen this one a million times, and I still get confused on it 🙂