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 score C and 25% for circuits given a quality score D.
(a) If a circuit failed, what is the probability that it had received a quality score either C or D?
(b) If a circuit did not fail, what is the probability that it had received a quality score A?