Question 11

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

If A and B are two independent events, prove that A’ and B 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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo