If at least one child in a family with 3 children is a boy w

If at least one child in a family with 3 children is a boy, what is the probability that at least 2 children are boys?

Let G shows the girl and B shows the boy. The sample space of 3 children will be

S = {GGG, GBG, GGB, BGG, GBB, BGB, BBG, BBB}

There are 7 outcomes that have at least 1 boy: GBG, GGB, BGG, GBB, BGB, BBG, BBB

There are 4 outcomes that have at least 2 boys: GBB, BGB, BBG, BBB

P(at least one boy) = 7/8

P(at least two boys and at least one boy) = P(at least two boys) = 4/8

So the probability that at least 2 children are boys given that at least one child in a family of 3 children is boy will be

P(at least two boys | at least one boy) =P(at least two boys and at least one boy) / P(at least one boy) = (4/8) / (7/8) = 4/7