(3) There is a factory producing springs for mattresses. This factory uses 3 machines, saying A, B, and C, and these machines make the same type of spring. The probability of producing defective products in each machine A, B, and C is 1%, 2%, and 3%, respectively. Also, among the total amounts of the springs made in this factory, 30% is made by A, 50% is made by B, and 20% is made by C. (a) [3pts] One day, the owner of the factory randomly chooses one of the springs, and checks its quality. Find the probability that this spring is defective. (Hint: Use Bayes' rule.) (b) [2pts] Sadly, the above spring is defective. Under this situation, nd the probability that this spring is a product of the machine B