Question: Quality control engineers monitor the number of nonconformances per car in an automobile production facility. Each day, a simple random sample of four cars from the first assembly line and a simple random sample of three cars from the second assembly line are inspected. The probability that an automobile produced in the first shift has zero nonconformances is 0.8. The corresponding probability for the second shift is 0.9. Find the probability of the events
(a) zero nonconformances are found in the cars from the first assembly line in any given day,
(b) the corresponding event for the second assembly line, and
(c) zero nonconformances are found in any given day. State any assumptions you use.