A foundry has 4 different production lines and wants to evaluate the performance

Question

A foundry has 4 different production lines and wants to evaluate the performance of each line. The performance of each line is given below: Parts from all 4 lines merge into a single conveyor to take them to inspection. Consider a part randomly picked from this conveyor. Use events W, X, Y, and Z, to represent that a part came from the respective line and D to represent that a part is defective. a) What is the probability that the part came from Line Y? b) What is the probability that the part came from Line W and is defective? c) Given that a part came from Line Z, what is the probability that it is defective?

Explanation / Answer

A) P(part came from line y) = 0.21

B) P(came from line w and defective) = 0.08

C) P(defective | part came from line z) = P(defective and came from line z) / came from line z = 0.01/0.28 = 0.036

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