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Math Help - basic question about probabililty = zero

  1. #1
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    basic question about probabililty = zero

    Suppose one asks what the probability is that a point on a sphere is on the equator? On one side, that would be zero, since the equator has measure zero on the sphere. On the other side, probability zero means that it is impossible, which it clearly isn't. What is the usual solution to this?
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    MHF Contributor FernandoRevilla's Avatar
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    Re: basic question about probabililty = zero

    Quote Originally Posted by nomadreid View Post
    On the other side, probability zero means that it is impossible,
    That is not true, choose for example the probability space (S,\mathcal{P}(S),p) with S=\{a,b\} and p defined by p(\{a\})=0, p(\{b\})=1 .
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  3. #3
    Grand Panjandrum
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    Re: basic question about probabililty = zero

    Quote Originally Posted by nomadreid View Post
    Suppose one asks what the probability is that a point on a sphere is on the equator? On one side, that would be zero, since the equator has measure zero on the sphere. On the other side, probability zero means that it is impossible, which it clearly isn't. What is the usual solution to this?
    Probability zero is not the same as impossible.

    CB
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    Re: basic question about probabililty = zero

    Thank you, FernandoRevilla and CaptainBlack. That answers my question.
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