If A & B are two events such that P(B) ≠ 1, B C denotes the event complementry to B, then
Mathematics · JEE Advanced · NTA Exams — Statistics and Probability
If A & B are two events such that P(B) ≠ 1, BC denotes the event complementry to B, then
- P\(\left(\mathrm{A} / \mathrm{B}^{\mathrm{C}}\right)\) = \(\frac{\mathrm{P}(\mathrm{~A})-\mathrm{P}(\mathrm{~A} \cap \mathrm{~B})}{1-\mathrm{P}(\mathrm{~B})}\)
- P (A ∩ B) ≥ P(A) + P(B) − 1
- P(A) > P\((\mathrm{A} / \mathrm{B})\) if P\(\left(\mathrm{A} / \mathrm{B}^{\mathrm{C}}\right)\) > P(A)
- P\(\left(\mathrm{A} / \mathrm{B}^{\mathrm{C}}\right)\) + P\(\left(A^{C} / B^{C}\right)\) = 1
Answer
(A) P ( A / B ^ C ) = P ( ~A )- P ( ~A ~B ) 1- P ( ~B ), (B) P (A ∩ B) ≥ P(A) + P(B) − 1, (C) P(A) > P ( A / B ) if P ( A / B ^ C ) > P(A), (D) P ( A / B ^ C ) + P (A^ C / B^ C ) = 1
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