You have made it to the final round of “Let’s Make a Deal.” You know that there is $1 million behind either door 1, door 2, or door 3. It is equally likely that the prize is behind any of the three...

You have made it to the final round of “Let’s Make a Deal.” You know that there is $1 million behind either door 1, door 2, or door 3. It is equally likely that the prize is behind any of the three doors. The two doors without a prize have nothing behind them. You randomly choose door 2. Before you see whether the prize is behind door 2, Monty chooses to open a door that has no prize behind it. For the sake of definiteness, suppose that before door 2 is opened, Monty reveals that there is no prize behind door 3. You now have the opportunity to switch and choose door 1. Should you switch?

Use a spreadsheet to simulate this situation 400 times. For each “trial” use an @Risk function to generate the door behind which the prize lies. Then use another @Risk function to generate the door that Monty will open. Assume that Monty plays as follows: Monty knows where the prize is and will open an empty door, but he cannot open door 2. If the prize is really behind door 2, Monty is equally likely to open door 1 or door 3. If the prize is really behind door 1, Monty must open door 3. If the prize is really behind door 3, Monty must open door 1.