UPSC NDA Math Model Paper 2

Let b stand for boy and g for girl.
The sample space S = {(b, b), (b, g), (g, b), (g, g)}
Let A = Both the children are boys
Let B = At least one of the child is boy.
i.e A = {(b, b)}, B = {(b, b), (b, g), (g, b)} and A ∩ B = {(b, b)}
⇒ P (B) = 3/4 and P (A ∩ B) = 1/4
As we know that, P(A|B)=

P(A∩B)

P(B)

⇒ P (A | B) = 1/3