Question: Refer to Example. Suppose you are appearing on a game show with a prize behind one of five closed doors: A, B,C, D, and E.
If you pick the right door, you win the prize. You pick door A. The game show host then opens one of the other doors and reveals that there is no prize behind it. Then the host gives you the option of staying with your original choice of door A or switching to one of the other doors that is still closed.
a. If you stick with your original choice, what is the probability that you will win the prize?
b. If you switch to another door, what is the probability that you will win the prize?
Example: The Monty Hall Problem
There are three doors on the set for a game show. Let's call them A, B, and C. If you pick the right door you win the prize. You pick door A. The host of the show, Monty Hall, then opens one of the other doors and reveals that there is no prize behind it. Keeping the remaining two doors closed, he asks you whether you want to switch your choice to the other closed door or stay with your original choice of door A. What should you do if you want to maximize your chance of winning the prize: stay with door A or switch-or would the likelihood of winning be the same either way?
