One of you I'm sure knows this classic puzzle:
I know the answer is you should always switch, but I can't remember the statistical reasoning behind it. Can someone remind me?
In a certain game show, a contestant is presented with three doors. Behind one of the doors is an expensive prize, behind the others is nothing. The contestant is asked to choose a door. The game show host, Monty, then opens one of the other doors to reveal a that there is nothing behind it. The contestant is then asked if she/he would like to stick with the original door or switch to the remaining door.
I know the answer is you should always switch, but I can't remember the statistical reasoning behind it. Can someone remind me?