Let’s Make a Deal

Marilyn is on the game show, “Let’s Make a Deal,” where she can win a brand new car if she selects the right door in a game. One of the doors contains the new car, and the other two doors each contain a goat.

Marilyn picks one of doors. Monty, the game show host, shows Marilyn a goat behind one of the doors that she did not pick. He asks her, “Of the two doors remaining, would you like to keep your first door, or switch to the other remaining door?”

What would you do in this situation? Design a simulation that will help you answer this question. Explain your experimental design and results.

Extension:
Determine and explain each of the probabilities for “staying” and “switching” doors in this situation.

Generalize this problem to n doors. Would your answers change? Explain.