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What are the odds ?

Discussion in 'Off Topic Threads' started by amboy49, Aug 17, 2009.

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  1. amboy49

    amboy49 Well-Known Member

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    Okay, the answers were compelling and accurate regarding the two mysterious doors to Hell or Nirvana.

    The other puzzler that was posed to the class still has me mystified and confused.

    Here we go:

    There are three boxes - marked A, B, and C. One of the boxes contains a million dollars ( or whatever you think is valuable. I suppose if the box(es) are big enough the "prize" could be the most desirable trap gun you can think of with custom exhibition wood fit and finished to your specicifications by the stock maker of your choice ! Imagine the possiblities ! )

    With no hints of any kind you are asked to select the box that you believe contains the "prize." Keep in mind the other two boxes are empty. No second or third place prize.

    Once you've selected a box ( either A, B, or C ) and before you are told if it contains the prize you are now informed that one of the other two boxes does NOT contain the prize.

    The question is : Do you stay with the original box you selected or switch to the remaining box you did not originally choose ?

    Obviously, when you made your first selection, the chances are one in three of being correct.


    Now with two boxes left, are the odds 50-50 or something different ?

    The instructor ( who happens to have a Ph.D. in statistics by the way ) provided the answer which I will share once I receive a few responses to the question i.e. stay with the box you picked first or switch once one of the boxes has been revealed to be empty.

    For purposes of the question, assume the first box you selected does NOT contain the prize.

    Hope I've explained this with enough clarity.

    Noel
     
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  2. Setterman

    Setterman Well-Known Member

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    Of the 2 boxes left....pick the one that looks like a K-80 gun case.
     
  3. amboy49

    amboy49 Well-Known Member

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    Sorry, all three boxes look identical. 8 >)
     
  4. paul e. stark

    paul e. stark TS Member

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    About three to one.
     
  5. trapshootin hippie

    trapshootin hippie Well-Known Member

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    Noel, you were told that "one of the other two boxes does NOT contain the prize." You weren't ASSURED that one of the remaining boxes DOES contain the prize. Correct?


    Gne J
     
  6. amboy49

    amboy49 Well-Known Member

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    One box does contain the prize.

    The real question is: do you stay with your original choice or do you switch to the box you didn't choose ?
     
  7. rocktire

    rocktire Member

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    He mentioned after you picked that ONE of the other TWO boxes does not contain your prize. He didn't say both of the other two boxes or neither of the other two boxes. I would switch boxes. Regardless of whether you switch or not your odds were 1 in 3 to begin with. And if he was telling you the truth that only 1 of the 2 boxes left contains the prize then you have narrowed it down making it 50/50 odds.
     
  8. Neil Winston

    Neil Winston Well-Known Member

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    Switch.

    I don't understand why. But maybe eight (edit: nineteen) years ago Ms. Vos Savant (billed as "the smartest woman in the world") posed just that question in her column in the Parade magazine which appears (or appeared) in some Sunday newspapers. She said "switch" and was deluged by "corrections," some from professors (and, presumably, professoresses) of statistics, one being, as I remember, at Princeton.

    She maintained her answer was correct and I think she turned out to be right, but I don't remember the train of logic that led to that proof.

    Neil

    edit: see the "Monty Hall Problem" in the link above.
     
  9. Barrelbulge(Fl)

    Barrelbulge(Fl) Banned User Banned TS Supporters

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    Stick with your first choice.
     
  10. dward

    dward Member

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    At first you have a 33% chance of picking the right box which makes the odds 66% that the prize is in the remaining two boxes. You state above that "you are now informed that one of the other two boxes does NOT contain the prize", but it's not clear if the exact box that is empty is identified.If they specifically identify the box that doesn't have the prize, it makes the odds now 66% that the prize is in the box not chosen and you should switch to that box. If they don't specifically identify the box that doesn't have the prize, the odds are even and your chances are the same with any of the boxes.

    With my luck it would make no difference as I would pick the box that contained a dried out Dog Squad turd from the Prez!
     
  11. halfmile

    halfmile Well-Known Member

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    I have to disagree with Lady Egghead.

    Once the empty box is removed, 1 of the 2 remaining are correct.

    While, indeed there was a 1/3 chance of being right at first, removing one changed the odds to 50-50.

    You can switch or keep your original selection and it doesn't matter, you are still picking one of the 2. You are making a new decision with 2 choices.

    Answer: 50-50.

    HM
     
  12. dward

    dward Member

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    To reinforce that the odds are better after they've removed the empty box...........what if there were 100 boxes and you picked one and they removed 98 empties from the other side.......would you still think your odds are even with the two remaining boxes? Or if you and I had three boxes to choose from and I always got to pick 2 to your one and they simply remove an empty from the two I have (which is guaranteed to be the case).........I like them odds!
     
  13. trapshootin hippie

    trapshootin hippie Well-Known Member

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    It seems that there is a play on words here. "One of the two other boxes does NOT contain the prize." It does not say that one of the remaining boxes DOES contain the prize, just that one does not. That could mean that neither of the boxes remaining contains the prize.
     
  14. amboy49

    amboy49 Well-Known Member

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    To all - thanks for the responses. Googling "Monty Hall" will bring up a ton of hits that goes into extraordinary detail and explanation re: this question.

    Amazing how such a "simple" question can bring up so much controversy.

    I suppose this is how they build all those big buildings in Vegas !

    Noel
     
  15. crusha

    crusha TS Member

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    I'm a little puzzled by your next-to-last sentence:

    "For purposes of the question, assume the first box you selected does NOT contain the prize."

    Uhhhh...if we're to assume the first box we picked doesn't contain the prize...isn't it a no-brainer to switch?


    I don't think that's how you meant to say it, but...
     
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