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

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  1. Class 12
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Transcript

Question 4 If A and B are two events such that P(A) = 0.2 , P(B) = 0.4 and P(A โˆช 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) = (๐‘ƒ(๐ด" โˆฉ " ๐ต))/(๐‘ƒ(๐ต)) Finding P (A โˆฉ B) Now, P(A โˆช B) = P(A) + P(B) โ€“ P(A โˆฉ B) 0.5 = 0.2 + 0.4 โ€“ P(A โˆฉ B) 0.5 = 0.6 โ€“ P(A โˆฉ B) P(A โˆฉ B) = 0.6 โ€“ 0.5 P(A โˆฉ B) = 0.1 Now, P(A|B) = (๐‘ƒ(๐ด" โˆฉ " ๐ต))/(๐‘ƒ(๐ต)) = 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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.