Dirk Schlimm
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.
Assuming you
want to maximize the chances for getting a great
prize, the question is: