A company involved in the integration of personal computers gets its graphics cards from three sources. The first source provides 20% of the cards, the second source 35%, and the third source 45%. Past experience has shown that 5% of the cards from the first source are found to be defective, while those from the second and third sources are found to be defective 3% and 2%, respectively, of the time.
(a) What percentage of the company's graphics cards are defective?
(b) If a graphics card is selected and found to be defective, what is the probability it was provided by the third source?