**The Monty Hall Problem**

**This problem is based on the game show, "Let's Make A Deal",
which starred Monty Hall. There was much discussion of this problem in
1990 and 1991 in the column "Ask Marilyn" in Parade Magazine.
Here is the problem: **

Suppose that you are on a game show, and you're given the choice of three doors. Behind one door is a car; behind the others, goats. You pick a door, say No.1, and the host, who knows what's behind the other doors, open another door, say No. 3, which has a goat. He then says to you, "Do you want to switch and pick door #2?" Is it to your advantage to switch?

We will study this problem using probability.

Trial | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |

Contestant
Chooses: |
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You Show Goat Under: | |||||||||||||||

Then Contestant
Chooses: |
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Did Contestant
Switch? |
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Did Contestant
Win or Lose? |

Total number of wins: _______ Total number of losses: ____________

Number of switch and win ____ Number of switch and lose __________

Number of stay and win ______ Number of stay and lose ____________

P(winning) = ________________ P(losing)=_________________________

P(winning | switch) = _______ P(winning | stay)= ________________

P(losing | switch) = ________ P(losing | stay)=__________________