The quality control chart of a certain manufacturing company shows that 45% of the defective parts produced in the company are due to mechanical errors and 55% were caused by human error. The defective parts caused by mechanical errors can be detected, with 95% accuracy rate, at an inspection station. The detection rate is only 80% if the defective parts are due to human error.
(a) Suppose a defective part was detected at the inspection station. What is the probability that this defective part is due to human error?
(b) Suppose that a customer returned a defective part that went undetected at the inspection station. What is the probability that the defective part is due to human error?