Question

A couple has two children, Find the probability that both children are males, if it is known that at least one of the children is male.

Answer 1

Let the events of having a boy and having a girl be A and B respectively, and denote them by B and G,

Then event A = both children are boys = {B, B}

B = at least one of the two children is a boy

= {BG, GB, BB}

∴ A ∩ B = {BB}

P(A ∩ B) = `1/4`

and  P(B) = `3/4`

∴ `P(A|B) = (P(A ∩ B))/(P(B))`

= `1/4 ÷ 3/4`

= `1/3`