Acertain system can experience three different types of defects. let ai (i = 1,2,3) denote the event that the system has a defect of type i. suppose that the following probabilities are true. p(a1) = 0.12 p(a2) = 0.07 p(a3) = 0.06 p(a1 ∪ a2) = 0.13 p(a1 ∪ a3) = 0.15 p(a2 ∪ a3) = 0.11 p(a1 ∩ a2 ∩ a3) = 0.01 (a) what is the probability that the system does not have a type 1 defect? (b) what is the probability that the system has both type 1 and type 2 defects? (c) what is the probability that the system has both type 1 and type 2 defects but not a type 3 defect? (d) what is the probability that the system has at most two of these defects?