A factory uses a diagnosis test to determine whether a part is defective or not. This test has a 0.90 probability of giving a correct result when applied to a defective part and a 0.05 probability of giving an incorrect result when applied to a non-defective part. It is believed that one out of every 1 000 parts will be defective.

(a) Calculate the posterior probability that a part is defective if the test says it is defective.

(b) Calculate the posterior probability that a part is non-defective if the test says it is non-defective.

(c) Calculate the posterior probability that a part is misdiagnosed.