I don't understand your point. I was arguing that the way the problem is posed seems to imply a unique solution. I was showing the problem was ill-posed, and th

I don't understand your point. I was arguing that the way the problem is posed seems to imply a unique solution. I was showing the problem was ill-posed, and that many probability problems have similar subtle or less subtle hidden assumptions. Here, this assumption is P(A, B | W) = P(A | W) P(B | W). I don't think you even need P(W = 0) = P(W = 1) = 0.5. These assumptions usually seem quite natural to make, but can be very unrealistic (why would the predictions of weather men be independent? I would bet they are not in reality). This is a very bad to teach students. It is always very important to know which assumptions you are making, and if textbooks do this wrong, it will be nearly impossible for students to get this right. I would think of a student which struggles with this problem as a better mathematician than the student which just uses P(A, B | W) = P(A | W) P(B | W) 'because the formula is in his textbook', but the second student is more likely to get rewarded (especially in American education, since the USA seems to be especially fond of textbooks which give a ready-made recipe for every problem that a student is supposed to solve).