42 lines
2.0 KiB
Plaintext
42 lines
2.0 KiB
Plaintext
[[File:Monte_Hall_problem.jpg|600px||right]]
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Suppose you're on a game show and you're given the choice of three doors.
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Behind one door is a car; behind the others, goats.
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The car and the goats were placed randomly behind the doors before the show.
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;Rules of the game:
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After you have chosen a door, the door remains closed for the time being.
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The game show host, Monty Hall, who knows what is behind the doors, now has to open one of the two remaining doors, and the door he opens must have a goat behind it.
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If both remaining doors have goats behind them, he chooses one randomly.
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After Monty Hall opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door.
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Imagine that you chose Door 1 and the host opens Door 3, which has a goat.
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He then asks you "Do you want to switch to Door Number 2?"
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;The question:
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Is it to your advantage to change your choice?
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;Note:
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The player may initially choose any of the three doors (not just Door 1), that the host opens a different door revealing a goat (not necessarily Door 3), and that he gives the player a second choice between the two remaining unopened doors.
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;Task:
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Run random simulations of the [[wp:Monty_Hall_problem|Monty Hall]] game. Show the effects of a strategy of the contestant always keeping his first guess so it can be contrasted with the strategy of the contestant always switching his guess.
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Simulate at least a thousand games using three doors for each strategy <u>and show the results</u> in such a way as to make it easy to compare the effects of each strategy.
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;References:
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:* Stefan Krauss, X. T. Wang, "The psychology of the Monty Hall problem: Discovering psychological mechanisms for solving a tenacious brain teaser.", Journal of Experimental Psychology: General, Vol 132(1), Mar 2003, 3-22 [https://doi.org/10.1037/0096-3445.132.1.3 DOI: 10.1037/0096-3445.132.1.3]
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:* A YouTube video: [https://www.youtube.com/watch?v=4Lb-6rxZxx0 Monty Hall Problem - Numberphile].
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<br><br>
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