1. Suppose you are on a game show in which there are 3 doors, exactly one of which will contain a terrific prize. The door that contains the prize will be decided randomly before the show, and each door has an equal chance of containing the prize. You are asked to pick a door, but you are not shown what is behind your door.
To be concrete, suppose you choose door 1. Your host then shows you one of the doors you did not pick, the only restriction being that the door you are shown must be empty. Say you are shown that door 2 does not have the prize.
want to maximize the chances for getting a great
prize, the question is: