A firm is involved in manufacturing high-quality electrical equipment. Each item produced costs £6000 and total annual output is 500 items. At the end of the production process each item is individually tested for quality and safety. If the item is defective in any way it is scrapped at a complete loss to the firm, since it has been found not cost-effective to repair such items. Historically, one item in 1000 is found to be faulty in some way.

(a) Determine the probability that the firm will produce zero faulty items in a year.

(b) Determine the probability that the firm will produce no more than three faulty items in a year.

(c) The firm is considering employing a quality inspector at an additional cost of

£1000 per year. The inspector, however, will be able to prevent any item from being defective. Suggest how the firm might evaluate whether employing the inspector would be cost-effective.