The Monty Hall Problem
Some months ago, I had the honor of interviewing Monty Hall for a story I was writing. If you don't know, Monty created and hosted one of TV's longest-running game shows, Let's Make a Deal. (non sequitur: I'm once again reminded of that hilarious exchange in Airplane II: Lloyd Bridges's character: "If anyone has any ideas - anything at all - now is the time to speak up." Jacob: "How about a game show like Hollywood Squares, but with kids? Gary Coleman could host.")
I'll post the answer after the jump, but I'd be interested to know what you think before you click through.
Once the host has opened a door, the car must be behind one of the two remaining doors. The player has no way to know which of these doors is the winning door, leading many people to assume that each door has an equal probability and to conclude that switching does not matter (Mueser and Granberg, 1999). This "equal probability" assumption, while being intuitively seductive, is incorrect. The player's chances of winning the car actually double by switching to the door the host offers.
For a very complex answer to WHY this is so, check out the full Wiki article, including a discussion of Bayes' theorem. If any of you recall my post on Mark Haddon's novel, the curious incident of the dog in the night-time, and have read the novel, you'll also find a pretty cool discussion of the Monty Hall Problem there.