Given: \(P(A/B) = P(B/A)\) and \(P(A/B) \ne 0\)
We know that \(P(A/B) = \frac{P(A \cap B)}{P(B)}\) and \(P(B/A) = \frac{P(A \cap B)}{P(A)}\)
Since \(P(A/B) = P(B/A)\), we have \(\frac{P(A \cap B)}{P(B)} = \frac{P(A \cap B)}{P(A)}\)
Since \(P(A/B) \ne 0\), it implies that \(P(A \cap B) \ne 0\). Therefore, we can safely divide both sides by \(P(A \cap B)\)
So, \(\frac{1}{P(B)} = \frac{1}{P(A)}\), which implies \(P(A) = P(B)\)
Correct Answer: P(A)=P(B)
AI generated content. Review strictly for academic accuracy.