Suppose P(A)= .45,P(B)= .20,P(C)= .35,P(E|A)= .10,P(E|B)= .05,and P(E|C)= 0.What is P(B|E)?
A)0.182
B)0.010
C)0.050
D)0.065
E)0.055

Question

Quizplus · Accepted Answer

To find P(B|E), use Bayes' theorem: P(B|E) = P(E|B)P(B) / P(E). First, calculate P(E) using the law of total probability: P(E) = P(E|A)P(A) + P(E|B)P(B) + P(E|C)P(C) = 0.10*0.45 + 0.05*0.20 + 0*0.35 = 0.045 + 0.01 + 0 = 0.055. Then, P(B|E) = (0.05*0.20) / 0.055 = 0.01 / 0.055 = 0.182.