A particular consumer product is being assembled on production lines A, B, and C and packaged in batches of 10. Each day, the quality control team selects a production line by probability sampling with probabilities P(A) = P(B) = 0.3 and P(C) = 0.4 and inspects a randomly drawn batch from the selected product line. The probability that no defects are found in a batch selected from production line A is .99, and the corresponding probabilities for production lines B and C are 0.97 and 0.92, respectively.

a) What is the probability that a batch from production line A is inspected and no defects are found?

b) Answer the above question for production lines B and C

c) What is the probability that no defects are found in any given day?

d) Given that no defects were found on a given day, what is the probability the inspected bath came from production line C?