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The Monty Hall Problem Options
Daemon
Posted: Sunday, April 8, 2018 12:00:00 AM
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The Monty Hall Problem

Named after the host of the game show Let's Make a Deal, the Monty Hall problem is a probability puzzle that has a history of stumping even respected mathematicians. In this problem, a game show contestant is asked to choose one of three doors. There is a car behind one and goats behind the other two. He picks door 1, but the host, who knows what is behind each door, opens door 3 to reveal a goat. The host then asks the player if he wants to switch to door 2. Should the player switch? More...
KSPavan
Posted: Sunday, April 8, 2018 2:40:01 AM

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The Monty Hall Problem
Named after the host of the game show Let's Make a Deal, the Monty Hall problem is a probability puzzle that has a history of stumping even respected mathematicians. In this problem, a game show contestant is asked to choose one of three doors. There is a car behind one and goats behind the other two. He picks door 1, but the host, who knows what is behind each door, opens door 3 to reveal a goat. The host then asks the player if he wants to switch to door 2.
pedro
Posted: Sunday, April 8, 2018 3:11:26 AM

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If he was behaving truly randomly he would frequently reveal a car whence the paradox disappears.

All good ideas arrive by chance- Max Ernst
ChristopherJohnson
Posted: Sunday, April 8, 2018 6:55:59 AM

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The topic was discussed and put to the test by Mythbusters, as far as I can remember.
phillman5
Posted: Sunday, April 8, 2018 12:35:56 PM
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"a probability puzzle that has a history of stumping even respected mathematicians" I would trend to say that is 'fake news' propagated by people trying to make this sound like a hard problem. The correct answer can easily be proved by a short Monte Carlo simulation (like less than 10 line) program in any programing language. The crux is the contestant's original choice still has only a 1/3 chance of being correct, where as Monte, knowing the correct answer, can always show the contestant a goat behind a door as there is always one available separate from whatever door the contestant chose; also Monte is not going to show him whats behind his door. After this 'preview', Monte has ADDED information that was not available at time of the original choice. With this added infomation it is wise to make another choice, and the contestant can go with his original pick which still has only a 1/3 chance of being correct (it hasn't changed as Monte knowingly can always shows a goat), or the only other choice is the other door, which now has a 50/50 chance of being correct. Any respectable mathematician should be able to root this out in less than 30 seconds of thinking, or they are no longer a respected mathematician.
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