A box contains m red balls and n green balls, where m and n are positive integers. A ball is drawn at random, replaced, and then a second ball is drawn. Using m and n only, answer the following:
a. (i) State the size of the sample space in terms of m and n for the two draws considered as ordered pairs.
b. (ii) Derive an expression for the probability that both balls drawn are red.
c. (iii) Derive an expression for the probability that both balls drawn are green.
d. (iv) Hence, obtain the probability that the two balls drawn are of different colours, simplifying your result as far as possible.