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Math Help - Probability Proof

  1. #1
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    Probability Proof

    Suppose that A and B are not trivial events, that is 0< P(A) < 1 and 0 , P(B) < 1. show that

    a. if A subset B, then A and B are not independent;

    b. if B subset A, then A and B are not independent;

    c. if A and B are disjoint then A and B are not independent
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  2. #2
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    Have you noticed that parts a & b are identical?
    a) P(B|A) = \frac{{P(B \cap A)}}{{P(A)}} = \frac{{P(A)}}{{P(A)}} = 1 \ne P(B).
    Do you see a contradiction therein if they were independent?

    A \cap B = \emptyset  \Rightarrow \quad P(A \cup B) = P(A) + P(B) - P(A \cap B) \Rightarrow \quad P(A \cap B) = 0
    Another contradiction???
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