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Thread: Conditional Probability and Complements

  1. #1
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    Conditional Probability and Complements

    P(A) = 4/9

    P(A|B) = 1/2

    P(A|B') = 1/3

    How do I go about finding P(B)?

    Thank you xxxx
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  2. #2
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    Re: Conditional Probability and Complements

    Quote Originally Posted by princessp View Post
    P(A) = 4/9, P(A|B) = 1/2, P(A|B') = 1/3
    How do I go about finding P(B)?
     \begin{align*}\mathcal{P}(A)&=\mathcal{P}(A\cap B)+\mathcal{P}(A\cap B') \\&=\mathcal{P}(A|B)\mathcal{P}(B)+\mathcal{P}(A|B  ')\mathcal{P}(B')\\&=\mathcal{P}(A|B)\mathcal{P}(B  )+\mathcal{P}(A|B')(1-\mathcal{P}(B))\end{align*}

    Now fill in the knowns, then solve for \mathcal{P}(B)
    Last edited by Plato; Jan 26th 2017 at 05:36 PM.
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