A product is being assembled and packaged on three production lines (line A, line B, and...

A product is being assembled and packaged on three production lines (line A, line B, and line C). Each day, the quality control team selects a production line and inspects a batch chosen at random from the output of the selected production line. Line A is selected with probability .5, line B is selected with probability .2, and line C is selected with probability .3. The probability that no defects will be found in a batch selected from line A is 0.98, and the corresponding probabilities for production lines B and C are 0.96 and 0.94, respectively.

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

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

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

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

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

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

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

Expert Solution

orchestra answered 1 year ago

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