Answer: According to Bayes’ Theorem, the probability of

QUESTION:

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

\(P(A \mid B)=\frac{P(A) \cdot P(B \mid A)}{P(A) \cdot P(B \mid A)+P\left(A^{\prime}\right) \cdot P\left(B \mid A^{\prime}\right)}\).

In Exercises 33–36, use Bayes’ Theorem to find \(P(A|B)\).

\(P(A)=\frac{3}{8}, P\left(A^{\prime}\right)=\frac{5}{8}, P(B \mid A)=\frac{2}{3}, \text { and } P\left(B \mid A^{\prime}\right)=\frac{3}{5}\)

Equation Transcription:

Text Transcription:

P(A|B)=P(A)P(B|A)P(A)P(B|A)+P(A')P(B|A')

P(A|B)

P(A)=frac{3}{8},P(A')=frac{5}{8},P(B|A)=frac{2}{3}, and P(B|A')=frac{3}{5}