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Math Help - Events A,B (independent, mutually exclusive), Help!

  1. #1
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    Events A,B (independent, mutually exclusive), Help!

    P(A/B)=0.2 , P(A/B^)=0.3 and P(B)=0.8

    a) Are the events A, B independent ?
    b) Are the events A, B mutually exclusive ?

    Can someone solve this exercise please ?
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  2. #2
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    I think it can be solved, here are some hints.

    Events A and B are independant if \displaystyle P(A\cap B) = P(A)\times P(B) , P(A/B) = P(A) , P(B/A) = P(B)

    Events A and B are mutually exclusive if \displaystyle P(A\cap B) = 0

    Now with the information given \displaystyle P(A/B) = \frac{P(A\cap B)}{P(B)} \implies 0.2 = \frac{P(A\cap B)}{0.8}\implies 0.16 = P(A\cap B)
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  3. #3
    MHF Contributor matheagle's Avatar
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    IF A and B are independent then

    P(A|B)=P(A)=P(A|B') which doesn't hold.
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