(P(A)=12 %, Pleft(A^{prime} ight)=88 %, P(B mid A)=66 %), and (Pleft(B mid A^{prime} ight)=19 %) According to...

\(P(A)=12 \%, P\left(A^{\prime}\right)=88 \%, P(B \mid A)=66 \%\), and \(P\left(B \mid A^{\prime}\right)=19 \%\)

According to Bayes' Theorem, the probability of event A, given that event B has occurred, is \(P(A \mid B)=\frac{P(A) \cdot P(B \mid A)}{P(A) \cdot P(B \mid A)+P\left(A^{\prime}\right) \cdot P\left(B \mid A^{\prime}\right)}\).
Use Bayes' Theorem to find \(P(A \mid B)\).