game show

You are a contestant on a game show and have won a shot at the grand prize. Before
you are three doors. $1,000,000 in cash has randomly been placed behind one door.
Behind the other two doors are the consolation prizes of dishwasher detergent. The
game show host asks you to select a door, and you randomly pick one. However,
before revealing the prize behind your door, the game show host reveals one of the
other doors that contains a consolation prize. At this point, the game show host asks
if you would like to stick with your original choice or to switch to the remaining
door.

Write a function to simulate the game show problem. Your function should
randomly select locations for the prizes, select a door at random chosen by the
contestant, and then determine whether the contestant would win or lose by
sticking with the original choice or switching to the remaining door. You may wish
to create additional functions invoked by this function.

Next, modify your program so that it simulates playing 10,000 games. Count the
number of times the contestant wins when switching versus staying. If you are the
contestant, what choice should you make to optimize your chances of winning the
cash, or does it not matter?