A warehouse contains 500 machines. Each machine is either new or used, and each machine has either good quality or bad quality. There are 120 new machines that have bad quality. There are 230 used machines. Suppose that a machine is chosen at random, with each machine being equally likely to be chosen.
(a) What is the probability that the chosen machine is a new machine with good quality?
(b) If the chosen machine is new, what is the probability that it has good quality?