Yes, this chestnut. Without the condition that one of the children be a boy, the sample space is
That one of the children is a boy eliminates the all-girl case, producing the three-outcome sample space
child 1 b b g g child 2 b g b g
It’s easy to distinguish the (b, g) and (g, b) outcomes: in one the brother is older than his sister, in the other he’s younger.? Under the assumption that sex selection is unbiased, and one child doesn’t influence the next, the sample space is symmetric, and each outcome has probability 1/3.
child 1 b b g child 2 b g b
The known boy has a brother in one of the three possible outcomes, for a 1/3 probability.