The organization that Jones works for is running a father–son dinner for those employees having at least one son. Each of these employees is invited to attend along with his youngest son. If Jones is known to have two children, what is the conditional probability that they are both boys given that he is invited to the dinner? Assume that the sample space S is given by S = {

(b, b),

(b, g ), ( g , b), ( g , g )} and all outcomes are equally likely [

(b, g ) means, for instance, that the younger child is a boy and the older child is a girl].