Here's a nice little probability problem that I first saw in David Darling's Universal Book of Mathematics:
You're in a game of Russian Roulette (with only one other player), but instead of one bullet the gun (a six-shooter revolver) is loaded with three bullets in three consecutive chambers. The barrel is spun only once. Each player points the gun at his head and pulls the trigger. If he is still alive, the gun is passed to the other player. The game ends when one player dies. Would you stand a better chance of surviving if you shot first or second, or does it make a difference?
This puzzle, or a variation of it, is often used as a brain teaser interview question. To avoid spoiling it for anyone, I'll add the solution as a comment to this post (so don't scroll down until you think you've worked it out).