Question
If $P(A|B) > P(A)$ , then which of the following is correct:
(A) $P(B|A) < P(B)$
(B) $P(A \cap B) < P(A) \cdot P(B)$
(C) $P(B|A) > P(B)$
(D) $P(B|A) = P(B)$
Probability — Class 12 Maths Solution
Step-by-step Solution
Option C is correct
$P(A|B) > P(A) \Rightarrow \cfrac{{P(A \cap B)}}{{P(B)}} > P(A)$
$\Rightarrow$ $P(A \cap B) > P(A) \cdot P(B) \Rightarrow \cfrac{{P(A \cap B)}}{{P(A)}} > P(B)$
$\Rightarrow$ $P(B|A) > P(B)$
NCERT & Exemplar solution for CBSE Class 12 Mathematics, Probability. Curated by Sachin Sharma. Free for all students.