(P(A)=73 %, Pleft(A^{prime} ight)=27 %, P(B mid A)=46 %), and (Pleft(B mid A^{prime} ight)=52 %) According to...

\(P(A)=73 \%, P\left(A^{\prime}\right)=27 \%, P(B \mid A)=46 \%\), and \(P\left(B \mid A^{\prime}\right)=52 \%\)

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 \(P(A \mid B)\).