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
$\displaystyle \begin{align*}\mathcal{P}(A)&=\mathcal{P}(A\cap B)+\mathcal{P}(A\cap B') \\&=\mathcal{P}(A|B)\mathcal{P}(B)+\mathcal{P}(A|B ')\mathcal{P}(B')\\&=\mathcal{P}(A|B)\mathcal{P}(B )+\mathcal{P}(A|B')(1-\mathcal{P}(B))\end{align*}$
Now fill in the knowns, then solve for $\displaystyle \mathcal{P}(B)$