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Get Those Brain Cells Working: The Monty Hall Problem

posted by janrinok on Friday July 29 2016, @10:27AM   Printer-friendly
from the something-to-think-about dept.

An Anonymous Coward writes:

Suppose you're 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 doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

Do any of you have any noteworthy experiences where knowledge of math helped you in an unusual way?

https://en.wikipedia.org/wiki/Monty_Hall_problem

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  • (Score: 2) by Gaaark on Friday July 29 2016, @04:46PM

    by Gaaark (41) Subscriber Badge on Friday July 29 2016, @04:46PM (#381605) Journal

    I look at it as:
    x. ?
    y. ?
    z. ?

    A door is revealed:
    You now have 2 doors with no clue/no information.
    Are you REALLY any closer to knowing if you should switch?

    I see it as going from 33.33333% repeating chance of having chosen correctly to 50% chance of having chosen correctly. Would switching really increase those odds? Isn't it really just 50%?
    Has any information been released to increase your odds?
    Not from where i'm standing (looking sharp in my banana suit with my stuffed monkey sitting on my shoulder).

    --
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  • (Score: 2) by VLM on Friday July 29 2016, @05:25PM

    by VLM (445) on Friday July 29 2016, @05:25PM (#381620)

    Are you REALLY any closer to knowing if you should switch?

    Yeah, but your numbers are too small or percentages are too large making it look weird.

    Assume it scales. Scale this to a billion doors. You pick a door which almost certainly isn't it. Dude opens a B-2 doors leaving a winner and a loser. The loser is almost certainly the one you picked, the winner is the remaining unopened door.

  • (Score: 2) by TheRaven on Friday July 29 2016, @05:56PM

    by TheRaven (270) on Friday July 29 2016, @05:56PM (#381635) Journal
    See my other reply to the parent, but the short form: If you pick correctly the first time, then switching will make you lose. If you pick incorrectly the first time, then Monty must close the one other door that is incorrect, so switching makes you win. You have a 1/3 chance of picking correctly the first time, a 2/3 chance of picking incorrectly. By switching, you flip those odds so you win if you picked incorrectly the first time and lose if you picked correctly.
    --
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