A family has two children. what is the probability that both the children are boys given that at least on of them is a boy?

1/3

Let b stands for boy and g for girl. The sample space of the experiment is

S= {(b, b), (g, b), (b, g), (g, g)}

let E and F denote the following events:

E: "both the children are boys"

F: "at least one of the child is a boy'"

Then E = {(b, b)} and F= {(b, b), (g, b), ((b, g)}

Now, E∩F  = {(b, b)}

Thus P(F) = 3/4 and P( E∩F) = 1/4

Therefore P(EIF) = P( E∩F)/ P(F)

                         = (1/4)/(3/4) 

                         = 1/3