Example 10 A die is thrown. If E is the event ‘the number appearing is a multiple of 3’ and F be the event ‘the number appearing is even’ then find whether E and F are independent ? Two events A and B are independent if P(A ∩ B) = P(A) . P(B) A die is thrown S = {1, 2, 3, 4, 5, 6} Let two events be E : the number appear is a multiple of 3 F : the number appearing is even E : {3, 6} P(E) = 2/6 = 1/3 F : {2, 4, 6} P(F) = 3/6 = 1/2 E ∩ F = the number appearing is an even multiple of 3 = {3} So, P(E ∩ F) = 1/6 Now, P(E) . P(F) = 1/3 × 1/2 = 1/6 Since, P(E ∩ F) = P(E) . P(F) Therefore, E & F are independent events

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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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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