Question 11

If A and B are two independent events, prove that A’ and B are also independent

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Question 11 If A and B are two independent events, prove that A’ and B are also independent Two events A and B are independent if P(A ∩ B) = P(A) . P(B) Now, P(A’ ∩ B) = P(not A and B) (Since A & B are independent events) = P(B) – P(A ∩ B) = P(B) – P(A) . P(B) = P(B) ( 1 – P(A)) ) = P(B) . P(A’) Since P(A’ ∩ B) = P(A’) . P(B) Hence, A’ & B are independent

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.