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If A and B are two events such that P(A) = 0.2 , P(B) = 0.4 and P(A ∪ B) = 0.5 , then value of P(A|B) is ?

(a) 0.1             (b) 0.25             (c) 0.5             (d) 0.08

If P(A) = 0.2 , P(B) = 0.4 and P(A U B) = 0.5, then value of P(A|B) is

Question 4 - CBSE Class 12 Sample Paper for 2020 Boards - Part 2

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Question 4 If A and B are two events such that P(A) = 0.2 , P(B) = 0.4 and P(A ∪ B) = 0.5 , then value of P(A|B) is ? (a) 0.1 (b) 0.25 (c) 0.5 (d) 0.08 We know that P(A|B) = (𝑃(𝐴" ∩ " 𝐵))/(𝑃(𝐵)) Finding P (A ∩ B) Now, P(A ∪ B) = P(A) + P(B) – P(A ∩ B) 0.5 = 0.2 + 0.4 – P(A ∩ B) 0.5 = 0.6 – P(A ∩ B) P(A ∩ B) = 0.6 – 0.5 P(A ∩ B) = 0.1 Now, P(A|B) = (𝑃(𝐴" ∩ " 𝐵))/(𝑃(𝐵)) = 0.1/0.4 = 1/4 = 0.25 So, correct answer is (c) 0.25 1 mark

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.