Question: 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 production line. The probability that no defects are found in a batch selected from production line A is 0.99, and the corresponding probabilities for production lines B and C are 0.97 and 0.92, respectively. A tree diagram may be used for answering the following questions.
(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 in a given day, what is the probability the inspected batch came from production line C?