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  1. #1
    Ryder Cup Winner Region3's Avatar
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    Maths / Probability Puzzle

    Heard this ages ago (I believe based on a real TV quiz show), but the Maths thread on here just reminded me of it.


    In the final of a quiz show there are 3 doors. Behind 1 door is the star prize and behind the other 2 are booby prizes.

    You are asked to pick a door as yours. The host then reveals a booby prize behind one of the 2 remaining doors, then asks you if you want to swap your door for the other remaining unopened one.

    Should you swap, or stick, and why?

  2. #2
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    Re: Maths / Probability Puzzle

    Stick as you have a 50/50 chance of the prize

    If you switch to one of the other doors it's still 33% chance

  3. #3
    Tour Winner MegaSteve's Avatar
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    Re: Maths / Probability Puzzle

    Quote Originally Posted by Region3 View Post
    Heard this ages ago (I believe based on a real TV quiz show), but the Maths thread on here just reminded me of it.


    In the final of a quiz show there are 3 doors. Behind 1 door is the star prize and behind the other 2 are booby prizes.

    You are asked to pick a door as yours. The host then reveals a booby prize behind one of the 2 remaining doors, then asks you if you want to swap your door for the other remaining unopened one.

    Should you swap, or stick, and why?
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  4. #4
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    Re: Maths / Probability Puzzle

    I would say swap. When you picked your door you had a 33% chance of it being right. You now have a 50% chance of the other door being the right one.

    Will be happy to admit if I'm wrong on this one as it's really just a guess on my part. Or does it not actually matter whether you swap or not as each door now has a 50% chance of being correct?

  5. #5

    Re: Maths / Probability Puzzle

    You switch because you have a 66% chance of winning. I know this because I was at the science centre and they told me.

  6. #6
    Challenge Tour Pro TheDiablo's Avatar
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    Re: Maths / Probability Puzzle

    You should always switch. It gives you a 2/3 chance of winning, when previously you had a 1/3 (and therefore have 1/3 chance when sticking). Same principle applies for shows such as Deal or No Deal - mathematically you should always switch.

  7. #7
    Ryder Cup Winner Region3's Avatar
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    Re: Maths / Probability Puzzle

    Quote Originally Posted by ColchesterFC View Post
    I would say swap. When you picked your door you had a 33% chance of it being right. You now have a 50% chance of the other door being the right one.

    Will be happy to admit if I'm wrong on this one as it's really just a guess on my part. Or does it not actually matter whether you swap or not as each door now has a 50% chance of being correct?
    2 ways of looking at it, and if I remember right there was disagreement between 2 branches of mathematics at the time.

    On the one hand you could say 2 doors, 1 star prize = 50% chance of winning.

    The way I look at it (as HowlingGale and TheDiablo above) is that if your gameplan is to swap no matter what then you win the star prize if you initially pick a booby prize (2/3) and win a booby prize if you initially pick the star prize (1/3).

  8. #8
    Tour Winner Maninblack4612's Avatar
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    Re: Maths / Probability Puzzle

    Quote Originally Posted by TheDiablo View Post
    You should always switch. It gives you a 2/3 chance of winning, when previously you had a 1/3 (and therefore have 1/3 chance when sticking). Same principle applies for shows such as Deal or No Deal - mathematically you should always switch.
    Seriously!?

    There's a 50% chance you have made the right choice. Makes no difference if you swop, you still have a 50:50 chance of being right.

    That is so obvious I can't believe anyone can think otherwise.
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  9. #9
    Tour Winner Kellfire's Avatar
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    Re: Maths / Probability Puzzle

    Quote Originally Posted by Maninblack4612 View Post
    Seriously!?

    There's a 50% chance you have made the right choice. Makes no difference if you swop, you still have a 50:50 chance of being right.

    That is so obvious I can't believe anyone can think otherwise.
    Statistically speaking you're wrong through.

  10. #10

    Re: Maths / Probability Puzzle

    I would rather open the box.

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