2. A box contains 3 red 5 blue and 2 green balls. A ball is repeatedly drawn from the box at random, its color recorded, and it is replaced back in the box. (a) Find the probability that at least one red ball appears before a blue ball. (b) Suppose that you stop drawing balls out of the box when the pattern red-bluered in consecutive draws appears for the rst time. That is, you stop drawing when red appears on the most recent die, blue appears on the second most recent die, and red appears on the third most recent die. Find the expected number of tosses needed. [15 marks]