A family has two children What is the conditional probabilit

A family has two children. What is the conditional probability that both are boys given that at least one of them is a boy? Denote by B the event that both children are boys; B = {b, b} and by s = sample space = {(b, b), (b, g), (g, b), (g, g)} and all outcomes are equally likely, [(b, g) means, for instance, that the older child is a boy and the younger child is a girl.]

Solution

Note that it is given that at least one is a boy, so we only consider the 3 results

{(b,b), (b,g), (g,b)}

in which, one event satisifies \"both are boys\".

Thus,

P(both are boys|at least one boy) = 1/3 or 0.333333 [answer]