Ex 13.3, 14 - Chapter 13 Class 12 - If A and B are two event - Ex 13.3

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  1. Chapter 13 Class 12 Probability
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Ex 13.3, 14 If A and B are two events such that A ⊂ B and P(B) ≠ 0, then which of the following is correct? (A) P(A|B) = P B﷯﷮P A﷯﷯ (B) P(A| B) < P(A) (C) P(A|B) ≥ P(A) (D) None of these Given, A ⊂ B So, A ∩ B = A P(A ∩ B) = P(A) Now, P(A|B) = 𝑃(𝐴 ∩ 𝐵)﷮𝑃(𝐵)﷯ P(B) = 𝑷(𝑨 ∩ 𝑩)﷮𝑃(𝐴|𝐵)﷯ P(B) = 𝑷(𝑨)﷮𝑃(𝐴|𝐵)﷯ Also, 0 < P(B) ≤ 1 0 < 𝑃(𝐴)﷮𝑃(𝐴|𝐵)﷯ ≤ 1 0 × P(A|B) < 𝑃(𝐴)﷮𝑃(𝐴|𝐵)﷯ × P(A|B) ≤ 1 × P(A|B) 0 < P(A) ≤ P(A|B) ∴ P(A|B) ≥ P(A) Hence , Option (C) is Correct

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