The probability of event $A$, given that event $B$ has occurred, can be found using Bayes's Theorem. $$ P(A \mid B)=\frac{P(A) \cdot P(B \mid A)}{P(A) \cdot PCB \mid A)+P\left(A^{\prime} ight) \cdot P\left(B \mid A^{\prime} ight)) $$ Use Bayes's Theorem to find $P(A \mid B)$ using the probabilities shown below. $$ P(A)=0.25, P\left(A^{\prime} ight)=0.75, PCB \mid A)=0.3, \text { and ) P\left( \mid A^{\prime} ight)=0.5 $$ The probability of event A, given that event B has occurred, is (Round to the nearest thousandth as needed.) S.P.PB. 331