Chapter 8.6, Problem 1E

In Exercises 1–8, use Bayes’ theorem or a tree diagram to calculate the indicated probability. Round all answers to four decimal places. [HinT: See Quick Example 1 and Example 3.]

$P\left(A|B\right)=.8,P\left(B\right)=.2,P\left(A{|B}^{\prime }\right)=.3$. Find $P\left(B|A\right)$.