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#1
11-22-2005, 02:51 AM
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Monty Hall Problem
While doing some research on the Bayes Theorem, I stumbled accross the Monty Hall Problem. It goes like this:
Monty Hall was the host of the TV game show, "Let's Make a Deal." Monty would have a contestant choose one of three doors. Behind two of the doors was a goat. Behind the third was a new car. Once the contestant made his pick, Monty, who knew which door the car was behind, would open up a door and reveal a goat. He would then give the contestant an opportunity to keep his pick or change it to the other door that had yet to be opened. The question is: Should the contestant change picks? The answer is: Yes The odds of the person initially making the right pick is 1/3. So if he makes the switch, he'll be right 2/3 of the time. 
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#2
11-22-2005, 02:52 AM
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Re: Monty Hall Problem
Excellent summary.
By the way, SEARCH is your friend
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#3
11-22-2005, 04:07 AM
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Re: Monty Hall Problem
[ QUOTE ]
While doing some research on the Bayes Theorem, I stumbled accross the Monty Hall Problem. It goes like this: Monty Hall was the host of the TV game show, "Let's Make a Deal." Monty would have a contestant choose one of three doors. Behind two of the doors was a goat. Behind the third was a new car. Once the contestant made his pick, Monty, who knew which door the car was behind, would open up a door and reveal a goat. He would then give the contestant an opportunity to keep his pick or change it to the other door that had yet to be opened. The question is: Should the contestant change picks? The answer is: Yes The odds of the person initially making the right pick is 1/3. So if he makes the switch, he'll be right 2/3 of the time. [/ QUOTE ] You forgot a crucial part of the description. If the car is behind the door initially chosen by the contestant, then Monty chooses randomly which door to open between the remaining two doors. You also didn't explain why the answer that the contestant should switch doors is the correct one (though I'm sure the MH problem has been discussed ad nauseum on this forum).
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#5
11-22-2005, 11:07 AM
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Re: Monty Hall Problem
[ QUOTE ]
You also didn't explain why the answer that the contestant should switch doors is the correct one [/ QUOTE ] Of course he did. He explained that staying give you 1/3. So changign give you 1-(1/3) = 2/3. 2/3 > 1/3. End of analysis of this very complicated problem...
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#6
11-22-2005, 08:24 PM
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Re: Monty Hall Problem
I think Bruce once said he was so tired of doing this he was going to delete any post that had the words 'three doors'
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#7
11-23-2005, 12:13 AM
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Re: Monty Hall Problem
[ QUOTE ]
[ QUOTE ] You also didn't explain why the answer that the contestant should switch doors is the correct one [/ QUOTE ] Of course he did. He explained that staying give you 1/3. So changign give you 1-(1/3) = 2/3. 2/3 > 1/3. End of analysis of this very complicated problem... [/ QUOTE ] No, he didn't. Here is what he said: "The answer is: Yes The odds of the person initially making the right pick is 1/3. So if he makes the switch, he'll be right 2/3 of the time." This is simply a statement of the correct answer, with no accompanying explanation as to why it is the correct answer.
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