4. A pharmaceutical product consists of 100 pills in a bottle. Two production lines used to the product are selected with probabilities 0.45 (line one) and 0.55 (line two). Each line can overfill or underfill bottles by at least 2 pills. Given that line one is observed, the probabilities are 0.02, 0.06, 0.88, 0.03, and 0.01 that the number of pills in the bottle will be 102, 101, 100, 99, and 98. For line two, the similar respective probabilities are 0.03, 0.08, 0.83, 0.04, and 0.02. (a) Find the probability that a bottle of the product will contain 98 pills. (b) Find the probability that a bottle of the product will contain 102 pills. (c) Given that a bottle contains the correct number of pills, what is the probability that it came from line one? (d) What is the probability that a purchaser of the product will receive less than 100 pills?