After production, an electrical circuit is given a quality score of A, B. C, or D. Over a certain period of time, 77% of the circuits were given a quality score A. 11% were given a quality score B, 7% were given a quality score C, and 5% were given a quality score D. Furthermore, it was found that 2% of the circuits given a quality score A eventually failed, and the failure rate was 10% for circuits given a quality score B. 14% for circuits given a quality given a quality score C, and 25% for circuits given a quality score D. Show all your work and circle your final answers. Use four decimal places for your calculations. a) Find the probability of a circuit failing. b) If a circuit failed, what is the probability that it had received a quality score either C or D?