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(A|E)?
A)0.045
B)0.190
C)0.818
D)0.100
E)0.055

Question

Quizplus · Accepted Answer

We can use Bayes' theorem:

P(A|E) = P(E|A) * P(A) / P(E)

We need to calculate P(E), which we can do 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
     = 0.055

Now we can substitute into Bayes' theorem:

P(A|E) = 0.10 * 0.45 / 0.055
       = 0.818 (rounded to three decimal places)

Therefore, the best answer is C.