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Math Help - Conditional Probability

  1. #1
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    Conditional Probability

    I have been working on two problems and keep confusing myself. Any help would be appreciated.

    Here they are....

    1) Let A and B be events from a sample space, with P(A)>0 and P(B)>0 and such that P(B|A)<P(B). Is it true that P(A|B)<P(A)?

    2) Let A and B be events from a sample space, with P(A)>0 and P(B)>0 and such that P(B|A)<P(A). Is it true that P(A|B)<P(B)?


    I know that if it is false, i need to have a counter example, but i am completely stuck on this. I keep confusing myself.
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  2. #2
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    Here's what I'm thinking:

    P(B|A) = \frac{P(BA)}{P(A)} < P(B)

    P(BA) < P(B)P(A)

     \frac{P(BA)}{P(B)} < P(A)

    P(A|B) < P(A)<br />
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  3. #3
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    This works for this one, but for the second one it will not. Therefore a counter-example will be needed. so how would i go about finding a counter-example.
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