A manufacturing plant makes radios that each contain an integrated circuit (IC) supplied by three sources A, B, and C. The probability that the IC in a radio came from one of the sources is 1/3, the same for all sources. ICs are known to be defective with probabilities 0.001, 0.003, and 0.002 for sources A, B, and C, respectively.
(a) What is the probability that any given radio will contain a defective IC?
(b) If a radio contains a defective IC, find the probability it came from source A.