After production, an electrical circuit is given a quality score of
A, B or C. Over a certain period of time, 70% of the circuits
were given a quality score A, 20% were given a quality score B,
10% were given a quality score C. 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 and
15% for circuits given a quality score C.
Given a circuit did not fail, what is the probability that it received a quality
score A?