A company buys components from two suppliers. One produces components that are of higher quality than the other. The high-quality supplier, call it Supplier A, has a defect rate of 2%. The low-quality supplier, Supplier B, has a defect rate of 10% but offers lower prices. This company buys in equal volume from both suppliers, with half of the orders going to each supplier.
(a) What is the probability that a component to be installed is defective?
(b) If a defective component is found, what is the probability it came from Supplier A?