Monty Hall hosted a game show called Let's Make a Deal. He presented his game show contestant with three doors numbered 1, 2, and 3. Behind one of the doors is the grand prize. The contestant chooses a door. Then Monty, who knows what's behind each door, opens up one of the two remaining doors which doesn't have the grand prize behind it. Monty then asks the contestant, "Do you want to stay with your original choice, or would you like to switch to the other remaining door?"

Should the contestant stay with her original choice, should she change to the other door, or does it not make any difference?