2 ms·

>We haven't added any artificial ordering into the problem. Yes you have! To run the experiment, you have to treat TH and HT as different but you "pretend" not

>We haven't added any artificial ordering into the problem. Yes you have! To run the experiment, you have to treat TH and HT as different but you "pretend" not to do so by adding them into the same pile. You're pretending to know that the father tells you which child is the "known boy", but by the statement of the problem, you don't know that. Why is this an error? Because the father must follow a rule - he must give you a boy, and there are two ways for him to do that in BB but you only recognize one. If you go the "table-minus" route, which both the author and your experiment do. But you can't do that without affecting the odds! By telling you they aren't both girls, he lowers the chance that either of them might be. Yes, I'm serious. Correct formulation of table: a) BG; b) GB; c) BB and he gives you the first; d) BB and he gives you the second.

ajanuary 13y ago
Isn't the probability of c and d half that of a and b? If BG is the case, there's 100% chance he's talking about the first child. If BB is the case, there's a 50% chance he's talking about the first one, and a 50% chance he's talking about the second one. BG, giving the first - 1/3 GB, giving the second - 1/3 BB, giving the first - 1/6 BB, giving the second - 1/6 [Edit] You're right. Tables can be a bad way of thinking about it, because you have to make sure each option has an equal probability for them to work. This is okay when you have a single variable (like in the original post), but gets tricky when you introduce a new variable (as you did: is the father thinking about the first or second). Once you get past one variable, trees are probably a better but still simple representation.