A Christmas draw aims to sell 5000 tickets, 50 of which will win a prize.

(a) A syndicate buys 200 tickets. Let X represent the number of these tickets that win a prize. (i) Justify the use of the Poisson approximation for the distribution of X. (ii) Calculate P(X < 3).

(b) Calculate how many tickets should be bought in order for there to be a 90% probability of winning at least one prize. (C)