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Math Help - Conditional probability proof

  1. #1
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    Conditional probability proof

    The question is:

    0 < P(A) < 1

    Show that if P(B given A) > P(B) then P(B given A') < P(B)
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  2. #2
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    Quote Originally Posted by sharpe View Post
    The question is:

    0 < P(A) < 1

    Show that if P(B given A) > P(B) then P(B given A') < P(B)
    P(B|A)=\dfrac{P(B\cap A)}{P(A)}>P(B)

    P(B|\overline{A})=\dfrac{P(B\cap \overline{A})}{P(\overline{A})}

    P(A)+P(\overline{A})=1

    P(B\cap A) + P(B\cap \overline{A})=P(B)

    Substitute..
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  3. #3
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    Quote Originally Posted by undefined View Post
    P(B|A)=\dfrac{P(B\cap A)}{P(A)}>P(B)

    P(B|\overline{A})=\dfrac{P(B\cap \overline{A})}{P(\overline{A})}

    P(A)+P(\overline{A})=1

    P(B\cap A) + P(B\cap \overline{A})=P(B)

    Substitute..

    Great thanks - that is very helpful and looks all too simple now - thanks!
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