Misc 13 If A and B are any two events such that P(A) + P(B) – P(A and B) = P(A), then (A) P(B|A) = 1 (B) P(A|B) = 1 (C) P(B|A) = 0 (D) P(A|B) = 0 Here P(A and B) = P(A ∩ B) Now, P(A) + P(B) – P(A and B) = P(A) P(A) + P(B) – P(A ∩ B) = P(A) P(B) – P(A ∩ B) = P(A) – P(A) P(B) – P(A ∩ B) = 0 P(B) = P(A ∩ B) P(B) = P(A ∩ B) Dividing By P(B) 1 = (𝑃(𝐴 ∩ 𝐵))/(𝑃(𝐵)) (𝑷(𝑨 ∩ 𝑩))/(𝑷(𝑩)) = 1 Also, P(A|B) = (𝑃(𝐴 ∩ 𝐵))/(𝑃(𝐵)) So, P(A|B) = 1 Hence, Option (B) is Correct.

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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.

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