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


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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.