Use Bayes' Theorem or a Tree Diagram to Calculate the Indicated

Multiple Choice

Use Bayes' theorem or a tree diagram to calculate the indicated probability. Round the answer to four decimal places. $P ( A \mid B ) = 0.8$ , $P ( B ) = 0.2$ , $P \left( A \mid B ^ { \prime } \right) = 0.3$ . Find $P ( B \mid A )$ .

A) $P ( B \mid A ) = 0.16$
B) $P ( B \mid A ) = 0.12$
C) $P ( B \mid A ) = 0.4$
D) $P ( B \mid A ) = 0.6$
E) $P ( B \mid A ) = 0.84$