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Example 13 - Prove that if E and F are independent, so are E and F'

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Example 13 Prove that if E and F are independent events, then so are the events E and F′. Two events A and B are independent if P(A ∩ B) = P(A) . P(B) Now, P(E ∩ F’) = P(E and not F) = P(E) – P(E ∩ F) = P(E) – P(E) . P(F) = P(E) ( 1 – P(F)) ) = P(E) . P(F’) Since P(E ∩ F’) = P(E) . P(F’) Therefore, the events E & F’ 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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.