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Math Help - Simple Bayes Problem

  1. #1
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    Simple Bayes Problem

    P(B) = 30\%
    P(B|P) = 40\%
    P(P|\bar{B}) = 13\%

    Solve for P(P|B)

    Can this be solved with the information given? I can calc joint probabilities P(P,\bar{B}) and P(\bar{P},\bar{B}), but I can't seem to figure out a variant of bayes law that will lead to the target probability.
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  2. #2
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    Re: Simple Bayes Problem

    Quote Originally Posted by VinceW View Post
    P(B) = 30\%
    P(B|P) = 40\%
    P(P|\bar{B}) = 13\%

    Solve for \mathcal{P}(P|B)

    From the given you can find \mathcal{P}(P).
    \begin{align*}\mathcal{P}(P)&=\mathcal{P}(P\cap B)+ \mathcal{P}(P\cap \overline{B})\\&= \mathcal{P}(B|P) \mathcal{P}(P)+\mathcal{P}(P|\overline{B})\mathcal  {P}(\overline{B}) \\&=(0.4) \mathcal{P}(P)+(0.13)(0.7)\end{align*} .
    Last edited by Plato; February 4th 2013 at 09:04 AM.
    Thanks from VinceW
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  3. #3
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    Re: Simple Bayes Problem

    Thanks Plato! That was the trick that I needed
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  4. #4
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    Re: Simple Bayes Problem

    I can calc joint probabilities P(P,\bar{B}) and P(\bar{P},\bar{B}), but I can't seem to figure out a variant of bayes.
    thanks for sharing.

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