The Wayne Manufacturing Company purchases a certain part from suppliers A, B, and C. Suppler A supplies 65% of the parts, B 20%, and C 15%. The quality of parts varies among the suppliers, with A, B, and C parts having ½%, 2% and 3% defective rates, respectively. The parts are used in one of the company's major products.
a. What is the probability that the company's major product is assembled with a defective part? Use the tabular approach to Bayes' theorem to solve. (Show all calculations to earn credit.)
b. When a defective part is found, what is the probability of supplier C being the source of the defective part? Use the tabular approach to Bayes' theorem to solve. (Show all calculations to earn credit.)