Probability "paradox" question I found this probability puzzle a day or two ago, but I don't think I believe the reasoning used in the solution that's given. There are four situations involving a family with 2 children. In each case, a statement is made about one of the children, and the question is "What is the probability that the other child is a girl?"* (It is assumed that, in general, boys and girls are equally probable, and that the probability of each child is independent.) The four cases are: One child is a younger daughter named Mary. One child is an older daughter named Mary. One child is a daughter. One child is a daughter named Mary. The first 2 are straight-forward: the probability is 1/2. For the third one, the answer given is 1/3. The reasoning is that there are three cases: boy-girl, girl-boy, girl-girl (the order indicating relative age). Here is the answer the page author gives for the fourth one: It depends on the probability of the mother naming both her children Mary. If she names all her children Mary then knowing one of them is named Mary doesn't help us and the answer as you know from question 3 is 1/3. If she names only one child Mary, then this uniquely identifies the child and the probability is 1/2. That is, there are two mutually exclusive possibilities: Mary is the older child or Mary is the younger child. In either case the probability of the other child being a girl is 1/2. Now I don't think I accept the reasoning on case 3 (I don't accept case 4 as it stands either, but that's because of the problem with 3). It seems to me that, for case 3, any reference to the relative ages of the children is irrelevant and the probability would still be 1/2. Suppose case 3 were stated thus: You meet a mother and daughter and they tell you there is one other child in the family. What is the chance that the other child is a girl?Why would this be different from case three? Or to ask the question differently, isn't this an essentially identical problem: There are two identical decks of cards. Out of your sight, someone draws a card from each deck, places them face down and removes the decks. You turn over one card and it's the 3 of diamonds, what is the chance that the other is a 3 of diamonds? To translate the answer to case 4 into the card scenario, it seems that the author is saying that the answer would change depending on whether or not you could tell the decks apart, which would make no sense, yes? In order to get a probability of 1/3, you would need a question like: A family has 2 children, one of which is named Mary (and the parents are stodgy types who wouldn't name a boy Mary; they also confuse easily - so they don't give their children identical names). You meet a girl from the family, what is the chance her name is not Mary? Does what I'm saying sound correct, or did I miss something? * This sentence was edited for clarity. It used to read: 'In each case, some information is given about one child, and the question is "What is the probability that the second child is a girl?"' The phrasing of the four statements was changed also - each used to start "There is..." rather than "One child is..."