It is estimated that, on average, one match in five in the Football League is drawn, and that one match in two is a home win.

(a) Twelve matches are selected at random. Calculate the probability that the number of drawn matches is (i) exactly three, (ii) at least four.

(b) Ninety matches are selected at random. Use a suitable approximation to calculate the probability that between 13 and 20 (inclusive) of the matches are drawn.

(c) Twenty matches are selected at random. The random variables D and H are the numbers of drawn matches and home wins, respectively, in these matches. State, with a reason, which of D and H can be better approximated by a normal variable. (C)