$\displaystyle P(B) = 30\%$

$\displaystyle P(B|P) = 40\%$

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

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.