Ex 13.1, 3 - Chapter 13 Class 12 Probability

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Ex 13.1, 3 If P (A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4, find (i) P(A ∩ B)P(A) = 0.8 , P(B) = 0.5 & P(B|A) = 0.4 Now, we know that P(B|A) = (𝑃(𝐵 ∩ 𝐴))/(𝑃(𝐴)) 0.4 = (𝑃(𝐴 ∩ 𝐵))/(𝑃(𝐴)) 0.4 = (𝑃(𝐴 ∩ 𝐵))/(0. 8) P(A ∩ B) = 0.4 × 0.8 P(A ∩ B) = 0.32 Ex 13.1, 3 If P (A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4, find (ii) P(A|B)P(A|B) = (𝑃(𝐴 ∩ 𝐵))/(𝑃(𝐵)) = 0.32/0.5 = 32/50 = 0.64 ∴ P(A|B) = 0.64 Ex 13.1, 3 If P (A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4, find (iii) P(A ∪ B)P(A ∪ B) = P(A) + P(B) – P(A ∩ B) = 0.8 + 0.5 – 0.32 = 1.3 – 0.32 = 0.98 ∴ P(A ∪ B) = 0.98