Question: A company produces light bulbs at three factories. First factory produces 30% of total number of bulbs, of which 2% are defective. Second factory produces 20% of total number of bulbs, of which 4% are defective. Third factory produces 50% of total number of bulbs, of which 5% are defective.

a) Find the probability that a randomly chosen bulb is defective.
b) If randomly chosen bulb is defective, find the probability that it's produced at the first factory.