Question. A company manufacturing electronic components for home entertainment sys- tems buys electrical connectors from three suppliers. The company prefers to use supplier A because only 1% of those connectors prove to be defective, but supplier A can deliver only 70% of the connectors needed. The company also must purchase connectors from two other suppliers, 20% from supplier B and the rest from supplier C. The rates of defective connectors from B and C are 2% and 4%, respectively. (a) What is the probability that a randomly selected component has a defective connector?

(b) Suppose you buy one of these components, and when you try to use it you find that the connector is defective. What is the probability that your component came from (1) supplier A? (2) supplier B? (3) supplier C?