Let \(P(E)\) denote the probability of event \(E\). Given \(P(A)=1, P(B)=\frac{1}{2}\), the value of \(P(A \mid B)\) and \(P(B \mid A)\) respectively are
\(\mathrm{P}(A \cup B)=P(\mathrm{a})+P(B)-P(A \cap B)\) \[\] \(1=1+\frac{1}{2}-P(A \cap B)\) \[\] \(P(A \cap B)=\frac{1}{2}\) \[\] \(P(A / B)=\frac{P(A \cap B)}{P(B)}=\frac{\frac{1}{2}}{\frac{1}{2}}=1\) \[\] \(P(B / A)=\frac{P(B \cap A)}{P(A)}=\frac{1 / 2}{1}=\frac{1}{2}\) \[\] Choice (D)\[\]
Reinforce your conceptual grasp with related questions from NIMCET 2012:
Take timed full-length mock tests with authentic question distributions, negative marking (+12/-3 in Math), and instant All India Rank calculation.
Start Free Mock Test Series →