WAYSAFE, a large retail supermarket, has a standard inspection policy that determines whether a shipment of produce will be accepted or rejected. Specifically, they examine 5 percent of the objects in any shipment received, and, if no defective produce is found in any of the items examined, the shipment is accepted. Otherwise, it is rejected. The items chosen for inspection are drawn randomly, one at a time, without replacement, from the objects in the shipment.

A shipment of 1,000 5-1b. bags of potatoes are received at the loading dock. Suppose that in reality, 2 percent of the 5-1b. bags have defective potatoes in them. The "objects" that are being inspected are bags of potatoes, with a bag of potatoes being defective if any of the potatoes in the bag are defective.

(a) Define an appropriate probability space for the inspection experiment.

(b) What is the probability that WAYSAFE will accept the shipment of potatoes?

(c) What is the expected number of defective bags of potatoes when choosing 5 percent of the bags for inspection in the manner described above?

(d) If the inspection policy is changed so that 10 percent of the objects will be inspected, and the shipment will be accepted only if no defectives are found, what is the probability that the shipment will be accepted?