Every working day Mr Driver pulls out from his drive on to a main road in such a way that there is a very small probability p that his car will be involved in a collision.

(a) Show that in a five-day week the probability that there will be no collision is (1 - p).

(b) State one assumption that is made in this calculation.

(c) Using a binomial expansion, show that the probability that there will be at least one collision in a five-day week is approximately 5p.

(d) Given that p 0.001, use a calculator to find the probability that Mr Driver will avoid a collision in 500 working days. (NEAB)