A family has 3 children. The probability that all the three children are girls, given that at least one of them is a girl is

Step-by-step solution

The sample space for the genders of three children contains all possible combinations of boys (B) and girls (G), yielding 2^3 = 8 outcomes: S = BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG . Let A be the event that all three children are girls, so A = GGG and n(A) = 1 . Let B be the event that at least one child is a girl. The complement B' consists of all three boys: B' = BBB and n(B') = 1 , hence n(B) = 8 - 1 = 7 . The conditional probability P(A|B) = P(A B) / P(B) . Since A B, A B = A and n(A B) = 1 . With P(A B) = 1/