Simple Bayes Problem

**VinceW** · February 4th 2013, 07:17 AM

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

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.

**Plato** · February 4th 2013, 08:01 AM

Originally Posted by VinceW

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

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

From the given you can find $\mathcal{P}(P)$ .
$\begin{align*}\mathcal{P}(P)&=\mathcal{P}(P\cap B)+ \mathcal{P}(P\cap \overline{B})\\&= \mathcal{P}(B|P) \mathcal{P}(P)+\mathcal{P}(P|\overline{B})\mathcal {P}(\overline{B}) \\&=(0.4) \mathcal{P}(P)+(0.13)(0.7)\end{align*}$ .

**VinceW** · February 4th 2013, 08:35 AM

Thanks Plato! That was the trick that I needed

**moneesharobin** · February 6th 2013, 07:38 AM

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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