Problem 2 (50 points). A population of 1,000 semiconductor wafers contains wafers made by three machines (A, B, and C). In the population, 430 wafers are from machine A, and 220 are from machine B. A wafer will either meet or not meet a thickness specification. For machine A, 90% of its products confirm the thickness specification. For machine B, 15% of its products do not confirm the thickness specification. For machine C, 94% of its products confirm the thickness specification. A wafer is chosen at random from the population. (A) If the wafer is from machine A, what is the probability that it is conforming? (B) If the wafer is conforming, what is the probability that it is from machine A? (C) If the wafer is conforming, what is the probability that it is not from machine C? (D) If the wafer is not from machine C, what is the probability that it is conforming?