Two different factories both produce certain automobile part. The probabbility that a component from the first factory is defective is 2%, and the probability that a component from the second factory is defective is 5%. In a supply of 180 of the parts, 100 were obtained from the first factory and 80 from the second factory.
a) What is the probability that a part chosen at random from the 180 is from the first factory?
b) What is the probability that a part chosen at random from the 180 is from the second factory?
c) What is the probability that a part chosen at random from the 180 is defective?
d) If the chosen part is defective, what is the probability that it came from the first factory?