Solution Found!
Solved: According to Bayes’ Theorem, the probability of
Chapter 3, Problem 35EC(choose chapter or problem)
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 \(P(A|B)\).
\(P(A)=0.25, P\left(A^{\prime}\right)=0.75, P(B \mid A)=0.3, \text { and } P\left(B \mid A^{\prime}\right)=0.5\)
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)=0.25,P(A')=0.75,P(B|A)=0.3, and P(B|A')=0.5
Questions & Answers
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 \(P(A|B)\).
\(P(A)=0.25, P\left(A^{\prime}\right)=0.75, P(B \mid A)=0.3, \text { and } P\left(B \mid A^{\prime}\right)=0.5\)
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)=0.25,P(A')=0.75,P(B|A)=0.3, and P(B|A')=0.5
ANSWER:Solution:
Step 1 of 2:
It is given that according to Bayes’ theorem, the conditional probability of event A given event B is given by
P(A/B)=
where
P(A)=0.25
P(0.75
P(B/A)=0.3
P(B/=0.5
Using these values we need to find the value of P(A/B).