Summer 2000

Dirk Schlimm

# Homework No. 9

Friday, July 21, 2000
Due Tuesday, July 25, 2000

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:

Do you want to stay with your original pick (door 1) or switch (to door 3)?

Pick one of the following answers, and justify your pick.

A) Stay with original pick (door 1 has a better chance of having the prize than door 3).

B) Switch (door 3 has a better chance of having the prize than door 1).

C) It doesn't matter (door 1 and door 3 have the same chance of having the prize)