A product is being assembled and packaged on three productionlines (line A, line B, and line C). Each day, the quality controlteam selects a production line and inspects a batch chosen atrandom from the output of the selected production line. Line A isselected with probability .5, line B is selected with probability.2, and line C is selected with probability .3. The probabilitythat no defects will be found in a batch selected from line A is0.98, and the corresponding probabilities for production lines Band C are 0.96 and 0.94, respectively.

a) What is the probability that the quality control teaminspects a batch from line A and finds no defects?

b) What is the probability that the quality control teaminspects a batch from line B and finds no defects?

c) What is the probability that the quality control teaminspects a batch from line C and finds no defects?

d) What is the probability that no defects are found in anygiven day?

e) Given that no defects were found in a given day, what is theprobability the inspected batch came from line A?

f) Given that no defects were found in a given day, what is theprobability the inspected batch came from line B?

g) Given that no defects were found in a given day, what is theprobability the inspected batch came from line C?