Refer to Example 9.1.3. Suppose you are appearing on a game show with a prize behind one

Chapter 9, Problem 20

(choose chapter or problem)

Refer to Example 9.1.3. 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?