A factory has two machines that produce bolts. Machine I produces 69% of the daily output of bolts, and 8% of its bolts are defective. Machine II produces 31% of the daily output, and 5% of its bolts are defective.
(a) What is the probability that a bolt selected at random will be defective?
(b) If a bolt is selected at random and found to be defective, what is the probability that it was produced by Machine I?