# Ex 13.3, 14 (MCQ) - Chapter 13 Class 12 Probability

Last updated at April 16, 2024 by Teachoo

Chapter 13 Class 12 Probability

Serial order wise

Last updated at April 16, 2024 by Teachoo

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