Amanufacturer of calculators buys integrated circuits from supplies a, b and c. fifty percents of the circuits come from a, 30% from b and 20% from c. one percent of the circuits supplied by a have been defective, 3% of bs have been defective and 4% of c has been defective in the past.

(a) suppose that a circuit is randomly selected. what is the probability that it is defective
(b) a circuit is selected at random and found to be defective. what is the probability it was manufactured by a?