If \( \mathrm{A} \& \mathrm{~B} \) are two events such that \( \mat...
If \( \mathrm{A} \& \mathrm{~B} \) are two events such that \( \mathrm{P}(\mathrm{B}) \neq 1, \mathrm{~B}^{\mathrm{C}} \) denotes the event complementary to \( \mathrm{B} \), then
(A) \( \mathrm{P}\left(\mathrm{A} / \mathrm{B}^{\mathrm{C}}\right)=\frac{\mathrm{P}(\mathrm{A})-\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{1-\mathrm{P}(\mathrm{B})} \)
\( \mathrm{P} \)
(B) \( P(\mathrm{~A} \cap \mathrm{B}) \geq \mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-1 \)
(C) \( \mathrm{P}(\mathrm{A})\mathrm{P}(\mathrm{A} / \mathrm{B}) \) according as \( \mathrm{P}\left(\mathrm{A} / \mathrm{B}^{\mathrm{C}}\right)\mathrm{P}(\mathrm{A}) \)
(D) \( P\left(A / B^{C}\right)+P\left(A^{C} / B^{C}\right)=1 \)
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