2. (a) Box I contains 3 red and 5 white balls. Box II contains 4 red and 2 white balls. A

ball is chosen at random from the first box and placed in the second box without

observing its colour. Then a ball is drawn at random from the second box. What is the

probability that it is white?

(b) If at least one child in a family of two children is a boy, what is the probability that

both children are boys?