The Stonebridge Tire Co. manufactures passenger car tires. The manufacturing process results in tires that are either first-quality tires, blemished tires, or defective tires. The proportions of the tires manufactured that fall in the three categories are \(.88, .09\), and .03 , respectively. The manufacturing process is such that the classification of a given tire is unaffected by the classifications of any other tires produced.

(a) A lot of 12 tires are taken from the assembly line and inspected for shipment to a tire retailer who sells only first-quality tires. What is the probability that all of the tires will be first-quality tires?

(b) For the lot of tires in part (a), what is the probability that there will be no defective tires among the 12 tires?

(c) What are the expected number of first-quality tires, blemished tires, and defective tires in the lot of 12 tires from part (a)?

(d) What is the probability that the 12 tires will contain 8 first-quality tires, 3 blemished tires, and 1 defective tire?