Two different factories both produce a certain automobile part. The probability that a component from the first factory is defective is 3%, and the probability that a component from the second factory is defective is 5%. In a supply of 160 of the parts, 100 were obtained from the first factory and 60 from the second factory. Required:
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?