You made an order for a product from a mail-order firm which considers possible events in filling an order A: wrong item sent, B: item lost in transit, and C: item damaged in transit. Assume that A is independent of both B and C and that B and C are mutually exclusive. The individual event probabilities are P(A) = 0.01, P(B) = 0.02, and P(C) = 0.06. For a randomly chosen product, what is the probability that at least one of these errors occurs?

A company regularly takes deliveries of a particular sensitive part from three subcontractors A, B, and C. The proportion of the product delivered that are good or defective differ from time to time. Subcontractors that deliver non-defective products are considered reliable in terms of quality and have high probabilities. A random sample from large recent total deliveries indicates 32% and 35% of the product came from subcontractors A and B, respectively. Moreover, the sample indicates the percentage of defectives are 2%, 4% and 3% for A, B, andfor C, respectively. In terms of quality, what is the probability corresponding to the most reliable subcontractor?

As a warehouse manager, it is your responsibility to inspect a large shipment of components for defects. Two independent random samples, each of size 25 of these components will be checked, and the shipment will be accepted if fewer than 4 of these components are defective in both samples. What is the probability of accepting a shipment containing 12% defectives?

A supplier of free-range chickens has a contract with a restaurant for delivery to meet its monthly anticipated demand of at most 2010 kg (boneless, edible weight). The monthly market demand is assumed to be distributed normal with a mean of 1800 kg and standard deviation of 115 kg. If the monthly delivery amount is met as per contract, what is the probability that the monthly demand is more than the expected amount?