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An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A consists of 4 outcomes, the number of outcomes that B must have so that A and B are independent, is (A) 2, 4 or 8 (B) 3, 6 or 9 A. 2,4 or 8 B. 3,6, or 9 C. 4 or 8 D. 5 or 10. Select the correct answer from above options

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Correct Answer - D We have, P(A)= 4 10 = 2 5 Suppose B has n outcomes. Then, P(B)= n 10 ,0<n<10. Since A and B are independent events. ∴P(A∩B)=P(A)P(B) ⇒P(A∩B)= 2 5 × n 10 = 2n/5 10 ⇒ 2n 5 is an integer between 0 ans 10 ⇒ n 5 is an integer between 0 and 5 ⇒n=5,10.

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