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Math Help - Stats Proof.

  1. #1
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    Stats Proof.

    Can anyone give help with this proof question.

    The question states:

    Let A and B be events with 0 < P(A) < 1 and 0 < P(B) < 1. B is said to favor A if P(A|B) > P(A).

    (i) Show that if B favours A, then A also favours B, i.e. if P(A|B) > P(A) then P(B|A) > P(B).

    (ii) Show that if B favours A, then B complement favours A complement, i.e. show that if P(A|B) > P(A) then P(A complement | B complement) > P(A complement).
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  2. #2
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    Oct 2010
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    if  P(A|B)>P(A)
    since  P(A|B)=\frac{P(AuB)}{P(B)}
    thus  \frac{P(AuB)}{P(B)}>P(A)
    rearranging the equation gives you \frac{P(AuB)}{P(A)}>P(B)

    As for question two here a hint  P(\bar(A)|\bar(B))=\frac{P(B)-P(AnB)}{P(B)}
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