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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.


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.

 Related External Resources

Article on the Monty Hall Problem
This New York Times piece describes the historical significance of this problem as it appeared on the game show Let's Make a Deal, and how Marilyn Vos Savant tackled the solution.

Marilyn is tricked by a game show host
This critical analysis and debate over Marilyn Vos Savant's solution to the Monty Hall problem questions whether she was considering all of the possibile outcomes in the game.

Monty Hall simulation [ java applet ]
This simulation helps you test out the investigation above.

Generalized Monty Hall [ java applet ]
This simulation tests the Monty Hall question for a varied number of doors.

A Bayesian Puzzler
You are given an envelope with $10, and are told that one envelope contains twice as much money as the other envelope. Should you switch?

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