> Now suppose we know simply that a man has two children and that one of them is a son. [snip] It follows that the sexes of his two children, ordered from oldest to youngest, are either BB, BG or GB. Since these cases are equally likely, and since only one of them involves having two boys, we would say the probability that the man has two boys is 1/3.
Errr. except these cases aren't equally likely - because the boy we know about could be either of the boys in the BB scenario, but only one either of the other two. So the probability is still 1/2.
Errr. except these cases aren't equally likely - because the boy we know about could be either of the boys in the BB scenario, but only one either of the other two. So the probability is still 1/2.