1. We have 2 opaque boxes, each containing 3 balls. One box has 2 red balls and 1 blue ball, the other has 1 red ball and 2 blue balls. You pick a box at random and then pick one of the balls in that box 6 marks) at random. When you look at the ball it is red. (a) What is the probability that the remaining two balls in this box have the same colour? (b) You then randomly pick a ball from the remaining two balls in this box, and it turns out to be blue. What is the probability that the last ba in this box is also blue? Show working. (Hint: You may use Baye's theorem to solve the problems.)