Answer
$P(B|A)=\frac{.8\times.2}{.8\times.2+.3\times .8}=.4$
Work Step by Step
Accordint to Bayes' theorem:
$P(A|B)=\frac{P(B|A)P(A)}{P(B|A)P(A)+P(B|A')P(A')}$
Here, we have
$P(A|B)= .8$
$P(B)= .2$
$P(A|B')= .3$
Be aware, that A and B are in the definition of the theorem.
We know, that $P(B')=1-P(B)=1-.2=.8$
We can substitute into the definition:
$P(B|A)=\frac{.8\times.2}{.8\times.2+.3\times .8}=.4$