A manufacturer makes three types of screws. Type A comes in a bulk pack of 1000 screws. Type B comes in a bulk pack of 500 screws. Type C comes in a bulk pack of 800 screws. Type A screws each have a probability of .001 of having a flaw. The probability is .003 for Type B and .005 for Type C.
(a) If a contractor buys one pack of each type of screws, find the expected total number of defective screws among the three packs.
(b) Find the probability that there are no more than 5 defective screws total among the three packs.
(c) Find the expected number of packs that have no more than 5 defective screws. (Your answer will be between 0 and 3.)