If A and B are two events such that \(P(A|B) = P(B|A)\), and \(A \cap B \ne \emptyset\) then
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(P(A) = P(B)\)
By the definition of conditional probability:
\( \displaystyle P(A|B) = \frac{P(A \cap B)}{P(B)},\quad P(B|A) = \frac{P(A \cap B)}{P(A)} \)
Equating the two:
\( \displaystyle \frac{P(A \cap B)}{P(B)} = \frac{P(A \cap B)}{P(A)} \)
Since \(A \cap B \ne \emptyset\), \(P(A \cap B) \ne 0\) and it can be cancelled:
\(P(A) = P(B)\)
NCERT (2026-27 edition):
Conditional Probability
