# Simple Bayes Problem

• Feb 4th 2013, 07:17 AM
VinceW
Simple Bayes Problem
$\displaystyle P(B) = 30\%$
$\displaystyle P(B|P) = 40\%$
$\displaystyle P(P|\bar{B}) = 13\%$

Solve for $\displaystyle P(P|B)$

Can this be solved with the information given? I can calc joint probabilities $\displaystyle P(P,\bar{B})$ and $\displaystyle P(\bar{P},\bar{B})$, but I can't seem to figure out a variant of bayes law that will lead to the target probability.
• Feb 4th 2013, 08:01 AM
Plato
Re: Simple Bayes Problem
Quote:

Originally Posted by VinceW
$\displaystyle P(B) = 30\%$
$\displaystyle P(B|P) = 40\%$
$\displaystyle P(P|\bar{B}) = 13\%$

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

From the given you can find $\displaystyle \mathcal{P}(P)$.
\displaystyle \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*}.
• Feb 4th 2013, 08:35 AM
VinceW
Re: Simple Bayes Problem
Thanks Plato! That was the trick that I needed
• Feb 6th 2013, 07:38 AM
moneesharobin
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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