View Poll Results: What's the odds it's under your first choice?

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  • 50%

    1 12.50%
  • 33.33...%

    7 87.50%
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Math Help - Pick a shell, any shell

  1. #1
    MHF Contributor Quick's Avatar
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    Smile Pick a shell, any shell

    Let's play the shell game. I mix up three identical shells, one has a ball under it. You choose a shell. Instead of showing you your shell, I lift up another one that I know doesn't have the ball. You then get to pick which shell you'll take. What is the probability that the ball is under your original shell.

    Now I say the answer is 50%

    However, my statistics book says the answer is 33%, because there was a 33% chance the ball was under the first one you chose. (which I see why that would be an opinion but I don't agree with it cause it seems like the choices are independent)

    What's your opinion?
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  2. #2
    MHF Contributor Quick's Avatar
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    BTW, I'm not referencing a school book. It's just a book on statistics.
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  3. #3
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    I am too lazy and bored to keep explaining the Monty Hall problem. Since I have the best explanation than anyone else I might post it here. But the book is correct the probability of staying is 33%.

    (What is so confusing about this Monty hall problem? People just cannot seem to solve it )
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  4. #4
    Member Glaysher's Avatar
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    Quote Originally Posted by Quick View Post
    Let's play the shell game. I mix up three identical shells, one has a ball under it. You choose a shell. Instead of showing you your shell, I lift up another one that I know doesn't have the ball. You then get to pick which shell you'll take. What is the probability that the ball is under your original shell.

    Now I say the answer is 50%

    However, my statistics book says the answer is 33%, because there was a 33% chance the ball was under the first one you chose. (which I see why that would be an opinion but I don't agree with it cause it seems like the choices are independent)

    What's your opinion?
    Shell 1, Shell 2, Shell 3

    Each with a probability of 1/3 that the ball is under

    Suppose you chose shell 1

    If the ball is under shell 1 then either shell 2 or shell 3 can be lifted and no extra information has been given

    If the ball is under shell 2 then shell 3 is lifted.

    If the ball is under shell 3 then shell 2 is lifted

    Three possibilities all with equal probability
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  5. #5
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by ThePerfectHacker View Post
    I am too lazy and bored to keep explaining the Monty Hall problem. Since I have the best explanation than anyone else I might post it here. But the book is correct the probability of staying is 33%.

    (What is so confusing about this Monty hall problem? People just cannot seem to solve it )
    I am not confused by that answer and so you don't have to explain it. I just wanted to see the opinion of everyone here.

    Quote Originally Posted by Glaysher View Post
    Shell 1, Shell 2, Shell 3

    Each with a probability of 1/3 that the ball is under

    Suppose you chose shell 1

    If the ball is under shell 1 then either shell 2 or shell 3 can be lifted and no extra information has been given

    If the ball is under shell 2 then shell 3 is lifted.

    If the ball is under shell 3 then shell 2 is lifted

    Three possibilities all with equal probability
    That was a much better approach then my book. All it said was "the 2/3 chance carries over"
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  6. #6
    TD!
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    Quote Originally Posted by Quick View Post
    I am not confused by that answer and so you don't have to explain it. I just wanted to see the opinion of everyone here.
    You're not confused by the correct answer? Then what's the problem? Googling for "Monty Hall problem" will give you many explanations. Mathematical answers don't work in a democratic way, it's not the majority answer which is right, it's just the correct one - so opinions don't really matter
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  7. #7
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    Quote Originally Posted by TD! View Post
    Mathematical answers don't work in a democratic way, it's not the majority answer which is right, it's just the correct one - so opinions don't really matter
    Finally someone who thinks like me. I hate it when people say it is 1/2 because they think it is a philosophical question (like in science) and you can choose sides. The same thing why the entire infinity thing makes me really angry, because there are nice formal definitions for infinity and people (the non-mathematical sub-human people) love to manipulate it until nothing makes sense.
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  8. #8
    Member Glaysher's Avatar
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    Quote Originally Posted by ThePerfectHacker View Post
    Finally someone who thinks like me. I hate it when people say it is 1/2 because they think it is a philosophical question (like in science) and you can choose sides. The same thing why the entire infinity thing makes me really angry, because there are nice formal definitions for infinity and people (the non-mathematical sub-human people) love to manipulate it until nothing makes sense.
    What infinity thing?
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  9. #9
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    Quote Originally Posted by Glaysher View Post
    What infinity thing?
    Here are some of the many versions....

    Ifinity minus infinity is zero because when you have infinite apples and you remove all of them you have left with none.

    One divided by zero is infinite because when finding the number of times zero goes into 1 is infinite because adding zero keeps producing zero.

    The log of a negative number is minus infinity because when you raise an exponent to a very large number you get zero.

    And so on....

    I am glad these guys are not mathemations.
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  10. #10
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ThePerfectHacker View Post
    I am glad these guys are not mathemations.
    Why? Do they give you a headache? Maybe you should apply some Head-On. Hahahahahahahahaha! (I just slay myself sometimes.)

    -Dan
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  11. #11
    Grand Panjandrum
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    Quote Originally Posted by topsquark View Post
    (I just slay myself sometimes.)
    In which case becoming a Samurai looks like a smart career move

    RonL
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  12. #12
    Senior Member TriKri's Avatar
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    Why would the probability increase when you show me an empty shell? I mean, that wasn't anything unexpected, was it? (O).(O)
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  13. #13
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    Quote Originally Posted by TriKri View Post
    Why would the probability increase when you show me an empty shell? I mean, that wasn't anything unexpected, was it? (O).(O)
    Consider 1,000,002 doors. 1 is good rest is bad. You pick one and 1,000,000 doors are shown to be false. You are left with 2 doors. Switch or no switch? Or do you say it no matter because you only have 2.
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  14. #14
    Senior Member TriKri's Avatar
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    Quote Originally Posted by ThePerfectHacker View Post
    Consider 1,000,002 doors. 1 is good rest is bad. You pick one and 1,000,000 doors are shown to be false. You are left with 2 doors. Switch or no switch? Or do you say it no matter because you only have 2.
    Exactly.
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  15. #15
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by TriKri View Post
    Exactly.
    Wikipedia gave me a better understanding of this problem (look under "Monty Hall Problem").

    There is a 1/3 chance you pick the right shell to begin with, therefore there is a 2/3 chance it's in another shell.

    The shell that is lifted up is merely a distraction, it changes nothing.
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