Chapter 3.2, Problem 34E

According to Bayes’ Theorem, the probability of event A, given that event B has occurred, is

$P(A|B)=\frac{P(A)\cdot P(B|A)}{P(A)\cdot P(B|A)+P(A^{\prime })\cdot P(B|A^{\prime })}.$

In Exercises 33–38, use Bayes’ Theorem to find P(A|B).

34. P(A) = $\frac{3}{8}$, P(A′) = $\frac{5}{8}$, P(B|A) = $\frac{2}{3}$, and P(B|A′) = $\frac{3}{5}$