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Math Help - The range of possible

  1. #1
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    The range of possible

    Conditional probability as below looks simple, but confused for me.

    P(A│B)=(P(A∩B))/(P(B))

    A. If P(AlB)=0.5, what is the range of possible P(A)?
    B. If P(AlB)=0.5, what is the range of possible P(B)?
    Last edited by tykim; August 5th 2012 at 11:13 PM.
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  2. #2
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    Re: The range of possible

    Quote Originally Posted by tykim View Post
    Conditional probability as below looks simple, but confused for me.
    P(A│B)=(P(A∩B))/(P(B))
    A. If P(AlB)=0.5, what is the range of possible P(A)?
    B. If P(AlB)=0.5, what is the range of possible P(B)?
    Here are some useful facts.
    P(A\cap B)=P(A|B)P(B)

    0\le P(A\cap B)\le  P(A)\le 1~\&~0\le P(A\cap B)\le  P(B)\le 1.
    Last edited by Plato; August 6th 2012 at 03:46 AM.
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  3. #3
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    Re: The range of possible


    Is it correct?

    It seems to be P(A│B)=P(A∩B)/P(B)
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  4. #4
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    Re: The range of possible

    Quote Originally Posted by tykim View Post

    Is it correct?

    It seems to be P(A\cap B)=P(A|B)P(B)
    See my edit.
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  5. #5
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    Re: The range of possible

    Dear Plato,

    Following your guidance,

    0≤P(A∩B)≤P(A)≤1
    0≤P(A│B)P(B)≤P(A)≤1
    0≤0.5P(B)≤P(A)≤1

    I can come to the below. How do you think?

    P(B)=0; 0≤P(A)≤1
    P(B)=1; 0.5≤P(A)≤1

    P(A)=0; P(B)=0
    P(A)=1; 0≤P(B)≤1
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