Ex 13.2, 8 - Chapter 13 Class 12 Probability

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Ex 13.2, 8 Let A and B be independent events with P (A) = 0.3 and P(B) = 0.4. Find (i) P(A ∩ B) (ii) P(A ∪ B) (iii) P (A|B) (iv) P (B|A) Two events A and B are independent if P(A ∩ B) = P(A) . P(B) Given, P(A) = 0.3 , P(B) = 0.4 • P(A ∩ B) = P(A) . P(B) = 0.3 × 0.4 = 0.12 ∴ P(A ∩ B) = 0.12 • P(A ∪ B) = P(A) + P(B) – P(A ∩ B) = 0.3 + 0.4 – 0.12 = 0.70 – 0.12 = 0.58 ∴ P(A ∪ B) = 0.58 • P (A|B) = 𝑃(𝐴 ∩ 𝐵)﷮𝑃(𝐵)﷯ = 0.12﷮0.40﷯ = 0. 3 ∴ P (A|B) = 0. 3 • P (B|A) = 𝑃(𝐵 ∩ 𝐴)﷮𝑃(𝐴)﷯ = 𝑃(𝐴 ∩ 𝐵)﷮𝑃(𝐴)﷯ = 0. 12﷮0. 30﷯ = 0.4 ∴ P (B|A) = 0. 4