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HallsofIvy
HallsofIvy is offline
#19
Jan20-05, 06:51 AM
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Quote Quote by matt grime
And why say marilyn was right when she got it wrong because she didn't know anything about conditional probablity? I trust you built the basic program to allow for the fact that the door they open is KNOWN to not have the car behind it?
A good reason to say Marilyn vos Savant was right is that she was!

I have no idea whether she did or did not know anything about conditional probability but her answer was correct. The question was "Suppose you choose one of three doors, knowing that there is a car behind one of them, equally likely to behind any one of the three doors. The game show host (Monty Hall) who knows which door the car is behind opens a door showing the car is not there. Would the person improve his/her chances of winning the car by changing his/her choice?

Marilyn vos Savant did not use conditional probability to answer: you did what mathematicians often do to think about a problem intially- look at an extreme case. She said "suppose there were 1000 door, with a car behind one of them. You choose one, the game show host opens 998 of the doors showing no car behind them. In other words, there are now two doors, your choice and one other, one having the car behind it. Would you change? You bet you would! Monty Hall has completely changed the odds, using his superior knowledge.
Of course, one can apply conditional probability to show that same result. I remember seeing this problem about 15 years ago as an exercise, in chapter one of an introductory probability book.

It is an interesting exercise to see what happens if Monty Hall does NOT know which door the car is behind but opens doors at random. You can use conditional probability to show that, in that case, given that the door he opens HAPPENS not to have the car behind it, there is no advantage to changing.