2. A certain system can experience three different types of defects. Let A1, A2, A3 denote the event that the system has a defect of type i. Suppose thatP(A1) = 0.12, P(A2) = 0.07, P(A3) = 0.05, P(A1 U A2) = 0.13, P(A1 U A3) = 0.14, P(A2 U A3) =0 .10 and P(A1 A2 A3) = 0 .01.a) What is the probability that the system does not have a type 1 defect? (2 pts)b) What is the probability that the system has both type 1 and type 2 defects? (2 pts)c) What is the probability that the system has both type 1 and type 2 defects but not a type 3 defect? (2 pts)d) What is the probability that the system has at most two of these defects? (2 pts)e) Find the conditional probability P(A2 | A1) the system has type 2 defect given the system has type 1 defect? (2 pts)f) Find the conditional probability P(A2C | A1) the system does not have 2 defect given the system has type 1 defect? (2 pts)g) Find the conditional probability P(A3 | A1C). (2 pts)h) Are A1 and A3 independent ? (2 pts)