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Thread: 3 Boxes Problem

  1. #1
    WiiChat Member Lewi T's Avatar
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    3 Boxes Problem

    You are playing a game. A person (game host) shows you 3 boxes. 1 box contains 100, 2 others are empty. You need to choose one of the boxes. If the box you chosen contains the money you win.

    Suppose you make a guess and point at some box. The game host instead of opening the box you just pointed at opens one of the other boxes and shows you that that box is empty. Then he asks "I'm going to give you a last chance to change your decision". So you can either stand by your original choice and point at the same box or choose the other one. What gives you better chances? (i.e. what are the chances you win if you choose the box you originally selected vs. the other box?)

  2. #2
    40lb box of rape ROB64's Avatar
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    I'd stay with my original choice. It's 50/50 either way, so it doesn't really matter unless you have x-ray vision.

  3. #3
    ミュージック Gikoku Harakami's Avatar
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    Quote Originally Posted by ROB64 View Post
    I'd stay with my original choice. It's 50/50 either way, so it doesn't really matter unless you have x-ray vision.
    Rob is right, it would just be a 50/50 chance. I too would stick with my original choice.

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  4. #4
    Anglophobiphile Brawny's Avatar
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    Haha, morons.

    edit: Think of it as two sides. There's your side, and the host side. When you choose one, the chance of having the hundred pounds in your side is 33% and his side is 66%. When he opens one of his and shows that it's empty and asks if you want to switch, you say yes, because his side still has a 66% chance of being the good box.

    Edit: In case the first line seemed too offensive, know that I thought this at first as well.
    Last edited by Brawny; 06-18-2009 at 08:22 PM.

  5. #5
    Novocain Stain'd ssbb_lover's Avatar
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    Wow, I was actually leaning towards Adam's answer. Definitely thought the same as y'all at first though.

    You guys should know that the answer isn't going to be that simple if Lewi posts an entire thread for it. :P

    Super Moderator - PM me if you have any issues.

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  6. #6
    Senior Member Napalmbrain's Avatar
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    Damn, Adam beat me to it. Yes, it is statistically better to change your answer (I've seen this problem before, with doors instead of boxes).



    I never add friend codes.

    Quote Originally Posted by AndThen?
    @ROB64 - The longer you spend on this forum, the more you realise that Napalmbrain knows a lot about everything.


  7. #7
    HITLER ME JEZ King Wiired's Avatar
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    I find this difficult to understand what you guys are saying?
    3 boxes, 33% chance of the £100 being in any of them.
    But if he shows you that 1 of the boxes are empty, then it's a 50% chance that your box is an empty one compared to the other 1..
    So switching it would still make a 50% chance surely.

    Unless you do all that 1/3 times a 1/2 statistics tree thing, but even that would come out the same?

  8. #8
    Kryptonightingale Sixty's Avatar
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    I think I'm stupid, because I'd still stick with my first choice.

  9. #9
    Senior Member Napalmbrain's Avatar
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    Quote Originally Posted by King Wiired View Post
    I find this difficult to understand what you guys are saying?
    3 boxes, 33% chance of the £100 being in any of them.
    But if he shows you that 1 of the boxes are empty, then it's a 50% chance that your box is an empty one compared to the other 1..
    So switching it would still make a 50% chance surely.

    Unless you do all that 1/3 times a 1/2 statistics tree thing, but even that would come out the same?
    Statistics is a quirky subject. This diagram explains how it works:

    Spoiler Alert!



    I never add friend codes.

    Quote Originally Posted by AndThen?
    @ROB64 - The longer you spend on this forum, the more you realise that Napalmbrain knows a lot about everything.


  10. #10
    HITLER ME JEZ King Wiired's Avatar
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    Oh yeah! I understand now. Thanks Napalm

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