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Assume that in a family, each child is equally likely to be a boy or a girl. A family with three children is chosen at random.

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Assume that in a family, each child is equally likely to be a boy or a girl. A family with three children is chosen at random. The probability that the eldest child is a girl given that the family has at least one girl is A. 1/2 B. 1/3 C. 2/3 D. 4/7 Select the correct answer from above options

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We can arrange the statement in set as S={(B,B,B),(G,G,G),(B,G,G),(G,B,G),(G,G,B),(G,B,B),(B,G,B),(B,B,G)} Let A be Event that a family has at least one girl then, A={(G,B,B),(B,G,B),(B,B,G),(G,G,B),(B,G,G)(G,B,G),(G,G,G) Let B be Event that eldest child is girl then, B={(G,B,B)(G,G,B),(G,B,G),(G,G,G) Now, (A ∩ B)={(G,B,B),(G,G,B),(G,B,G,)(G,G,G)

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