A certain system can experience three different types of defects. Let A; (i = 1,2,3) denote the event that the system has a defect of type i. Suppose that P(A1) = 0.3, P(A2) = 0.34, P(A3) = 0.31, = P(AUA2) 0.54, P(A UA3)=0.57, = P(A2 A3) 0.59, P(A1 A2 A3) = 0.02 (a) Find the probability that the system has exactly 2 of the 3 types of defects. (b) Find the probability that the system has a type 1 defect given that it does not have a type 2 defect and does not have a type 3 defect.