The Wayne Manufacturing Company purchases a certain part from suppliers A, B, and C. Supplier A supplies 60% of the parts, B 30%, and C 10%. The quality of parts varies among the suppliers, with A, B, and C parts having 0.25%, 1%, and 2% 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.

b. When a defective part is found, which supplier is the likely source?