Another similar problem from http://www.inference.phy.cam.ac.uk/mackay/itila/ http://www.inference.phy.cam.ac.uk/mackay/itila/ You visit a family whose three c

Another similar problem from http://www.inference.phy.cam.ac.uk/mackay/itila/ http://www.inference.phy.cam.ac.uk/mackay/itila/ You visit a family whose three children are all at the local school. You don't know anything about the sexes of the children. While walking clumsily round the home, you stumble through one of the three unlabeled bedroom doors that you know belong, one each, to the three children, and find that the bedroom contains girlie stuff in sufficient quantities to convince you that the child who lives in that bedroom is a girl. Later, you sneak a look at a letter addressed to the parents, which reads `From the Headmaster: we are sending this letter to all parents who have male children at the school to inform them about the following boyish matters'. These two sources of evidence establish that at least one of the three children is a girl, and that at least one of the children is a boy. What are the probabilities that there are (a) two girls and one boy; (b) two boys and one girl?