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Math Help - one probability prove question

  1. #1
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    one probability prove question

    Suppose that P(A)=a and P(B)=b. show that P(A|B)>=(a+b-1)/b.
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  2. #2
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    http://www.mathhelpforum.com/math-he...ial-19060.html
    Please, please learn to post in symbols? You can use LaTeX tags.
    [tex]P(A|B)\ge \dfrac{a+b-1}{b} [/tex] gives P(A|B)\ge \dfrac{a+b-1}{b} .
    Having misread this posting, I wasted a good bit of time.

    All it takes is to notice P(A\cap B)\ge P(A)+P(B)-1.
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  3. #3
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    Quote Originally Posted by Plato View Post
    http://www.mathhelpforum.com/math-he...ial-19060.html
    Please, please learn to post in symbols? You can use LaTeX tags.
    [tex]P(A|B)\ge \dfrac{a+b-1}{b} [/tex] gives P(A|B)\ge \dfrac{a+b-1}{b} .
    Having misread this posting, I wasted a good bit of time.

    All it takes is to notice P(A\cap B)\ge P(A)+P(B)-1.
    sry, how do you notice this?
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  4. #4
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    Quote Originally Posted by wopashui View Post
    sry, how do you notice this?
    Have you studied the axioms of probability?
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  5. #5
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    this is not one of the axioms of probability, is it, I'm afraid that we need to prove this is true before we use it
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  6. #6
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    Quote Originally Posted by wopashui View Post
    this is not one of the axioms of probability, is it, I'm afraid that we need to prove this is true before we use it
    Well you surely know that P(A\cup B)=P(A)+P(B)-P(A\cap B)
    AND \left( {\forall X} \right)\left( {0 \leqslant P(X) \leqslant 1} \right).

    Put it together for yourself.
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