This is sort of right but there are some underlying assumptions that it glosses over. Situation (a): We take a set of parents which all have 2 children. Select the group in which the youngest is a boy. What fraction of that group has two boys? 1/2, as stated in your first situation. Situation (b): Take a set of parents which all have 2 children. Select the group in which at least 1 is a boy and send the others home. What fraction of that group has two boys? 1/3, as stated in your second situation. Situation (c): Take a set of parents which all have 2 children. Select a group in which the youngest is a boy and send the others home. Tell the stranger "one of them is a boy". What fraction of that group two boys? The GGs and BGs left, the BBs and GBs stayed. So it's 1/2, same as situation (a). Situation (d): Take a set of of parents which all have 2 children. Have them pick one of their kids at random. If the kid they picked is a girl, send them home. Keep the remainder and tell the stranger of these parents children, "one of them is a boy" (which is true). What fraction of that group has two boys? 1/2, same as (a). The GGs all left, the BBs all stayed, half the BG and half the GB stayed, the pool will be equally divided between 2 boys and 1boy/1girl. In situations (c) and (d) we generated the samples in different ways, but phrased the statement in accordance with situation (b). Misleading maybe, but not technically wrong. The manner in which the children were selected guaranteed that at least 1 would be a boy. The normal intuition (at least my intuition) in the "one of them is a boy" statement is that the parent picked a one of their children at random and then stated its sex (first part of situation (d)). Were that the case, the probability of the other child being a boy would be 1/2. What this comes down to is the sample generating process matters, and the language describing a problem contains clues but they may not be fully fleshed out. This is known as the "Boy or Girl Paradox", see wikipedia for more details.