Given P (A)= 0.40, P (B)= 0.50, P (A $\cap$B)= 0.15.Find P (B|A).
A)0.20
B)0.80
C)0.30
D)0.375
E)0.15

Question

Quizplus · Accepted Answer

By Bayes' theorem:
P(B|A) = P(AF1F1F1S1F1F1F10 B|A) / P(A)
Since AF1F1F1S1F1F1F10 B = (AF1F1F1S1F1F1F1)0 B,
P(AF1F1F1S1F1F1F10 B|A) = P(AF1F1F1S1F1F1F1)0 B|A) P(F1F1F1S1|AF1F1F1) P(F1F1F10|BF1F1F1S1)
= [1 - P(AF1F1F1S1F1F1F1|A)] P(F1F1F1S1|A) P(F1F1F10|B)
= [1 - P(F1F1F1S1|A)P(F1F1F1|A)] P(F1F1F1S1|A) P(F1F1F10|B)
= [1 - 0.4*0.4] * 0.15 / 0.4
= 0.375
Therefore, the answer is D) 0.375.

Given P (A)= 0 ∩\cap∩ B)= 015Find P (B|A)

Given P (A)= 0 $\cap$ B)= 015Find P (B|A)