You are on a game show in which there are 3 doors. Behind one door is a pot of gold, but the other doors contain rocks. You choose door #1.
The host of the game show pulls a lever which will randomly open one of the two doors you didn't choose. To your relief, door #3 was opened and turned out to have rocks!
The host offers you a decision: stick with door #1, or switch to door #2. To maximize the probability that you get the gold, what should you do?