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Misc 19 - If P(A) + P(B) - P(A and B) = P(A), then P(B|A) - Miscellaneous

Misc 19 - Chapter 13 Class 12 Probability - Part 2

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Misc 19 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 = ( ) ( ) ( ) ( ) = 1 Also, P(A|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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.