1. A store has light bulbs from two suppliers, 1 and 2. The chance of supplier 1 delivering defective bulbs is 10%, whereas supplier 2 has a defective rate of 3%. Suppose 60% of the current supply of light bulbs came from supplier 1. If one of these bulbs is taken from the current supply and observed to be defective, ?nd the probability that it came from supplier 2.
2. 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?