23. From the set of all families with two children, a family is selected at random and is found to have a girl called Mary. We want to know the probability that both children of the family are girls. By Example 3.2, the probability should apparently be 1/3 because presumably knowing the name of the girl should not make a difference. However, if we ask a friend of that family whether Mary is the older or the younger child of the family, upon receiving the answer, we can conclude that the probability of the other child being a girl is 1/2. Therefore, there is no need to ask the friend, and we conclude already that the probability is 1/2! What is the flaw in this argument? Explain.