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    Conditional probability problem




    Given P(A1) = .12, P(A2) = .07, P(A3) = .05, P(A1 U A2) = .13, P(A1 U A3) = .14, P(A2 U A3) = .10, and P(A1 A2 A3) = .01

    What is the probability (A1 A2 A3 | A1) ?

    What is the probability (A1 | A1 U A2 U A3) ?

    What is the probability (A3(complement) | A1 A2)?

    I have been working on these problems for over an hour. I made a venn diagram, but it is wacky. I am also confused how to treat situations such as P ((A1 A2 A3) A1) like in the first problem.

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    Re: Conditional probability problem


    Use the formula

    P(A union B) = P(B) + P(B) - P(A intersect B).

    to compute probabilities of all "sub-unions". Then use

    P(A | B) = P(A intersect B) / P(B)

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