Question: 1. In the setup of a manufacturing process, a machine is either correctly or incorrectly adjusted. The probability of correct adjustment is 0.90. When correctly

1. In the setup of a manufacturing process, a machine is either correctly or incorrectly adjusted. The probability of correct adjustment is 0.90. When correctly adjusted, the machine operates with a 5% defect rate. However, if it is incorrectly adjusted, it has a defect rate of 75%. Defects are independent, conditional on the adjustment of the machine.

a. After the machine starts a production run, what is the probability that a defect is observed when one part is tested? (0.5 points)

b. Suppose that the one part selected by an inspector is found to be defective. What is the probability that the machine is incorrectly adjusted? (1 point)

c. After seeing one defective part, a second part is tested and found to be good. What is the revised probability that the machine is incorrectly adjusted given this information? (1 point)

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