Good read. Probability can be so counter-intuitive. One thing that's helped me a lot is seeing the log reciprocal relation between probability of an event, and the information in it. If I tell you that of Susan's two children, at least one is a girl, then I have given you log2(4/3) bits of information.(there are 3 of 4 possibilities where at least one is a girl, take reciprocal and log) If on the other hand you see the older one, and see she is a girl, you have gained log2(4/2) bits of information. (50/50 chance the other one is) Where does the extra information come from in the latter case? It comes from you having the which-child information you don't have in the first one: You know the older child is the one that's a girl. It gets a little weird though when you see a child of Susan who is a girl, but don't know which it is in terms of the predefined younger/older variable. You're back to the log(4/3) bits of information. Its a weird way to look at the world.
