2. In a factory, production line A,B and C are all producing boxes with the same size. On their production, production line A, B and C produce 1%, 2% and 3% defective boxes, respectively. Of the total production, line A produces 25%, line B produces 35% and line C produces 40%. A box is selected randomly from the total production of a day
a) what is the probability that it is defective?
b) if the box is defective, what is the conditional probability that it was produced by line C?