Simulating the Monty Hall problem that once attracted much

QUESTION:

Problem 17BSC

Simulating the Monty Hall Problem A problem that once attracted much attention is the Monty Hall problem, based on the old television game show Let’s Make a Deal, hosted by Monty Hall. Suppose you are a contestant who has selected one of three doors after being told that two of them conceal nothing but that a new red Corvette is behind one of the three. Next, the host opens one of the doors you didn’t select and shows that there is nothing behind it. He then offers you the choice of sticking with your first selection or switching to the other unopened door. Should you stick with your first choice or should you switch? Develop a simulation of this game and determine whether you should stick or switch. (According to Chance magazine, business schools at such institutions as Harvard and Stanford use this problem to help students deal with decision making.)