Q1 of 12 Page 13

If A and B are two independent events, prove that A′ and B are also independent.[CBSE 2017]

It is given that A and B are independent


Therefore, P(AꓵB) = P(A)P(B)


Now, P(A’ꓵB) = P(B) – P(AꓵB)


= P(B) – P(A)P(B)


= P(B)(1 – P(A))


= P(A’)P(B)


As, P(A’ꓵB) = P(A’)P(B)


Therefore, A, and B are independent.

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A die, whose faces are marked 1, 2, 3, in red and 4, 5, 6 in green, is tossed. Let A be the event “number obtained is even” and B be the event “number obtained is red”. Find if A and B are independent events.[CBSE 2017]

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A speaks truth in 75% and B in 80% of the cases. In what percentage of cases are they likely to contradict each other in narrating the same incident?[CBSE 2013]

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Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that (i) the youngest is a girl, (ii) at least one is a girl?[CBSE 2014]

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