A certain system can experience three different types of defects. Let A, denote the event that the system has a Type 1 defect, A2 denote the event that the system has a Type 2 defect, and A3 denote the event that the system has a Type 3 defect. You are given that: P(A1) = 0.12 P(A2) = 0.07 P(A3) = 0.05 P(A 1 U A2) = 0.13 P(A, U A3) = 0.14 P(A2 U A3 ) = 0.10 P(A ] n A2 n A3) = 0.01 a) Draw out the Venn diagram that represents the sample space and provide the probabilities for all the regions. Provide the set notation for each region. b) What is the probability that the system has exactly 2 defects? c) What is the probability that the system has at most two defects