Chapter 8.6, Problem 3E

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.]

$P\left(X|Y\right)=.8,P\left(Y^{\prime }\right)=.3,P\left(X{|Y}^{\prime }\right)=.5$. Find $P\left(Y|X\right)$.