Mathematics, 09.10.2019 22:00, iBrain

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) = 0.14 p(a2) = 0.09 p(a3) = 0.09 p(a1 ∪ a2) = 0.16 p(a1 ∪ a3) = 0.18 p(a2 ∪ a3) = 0.14 p(a1 ∩ a2 ∩ a3) = 0.02 (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?

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Acertain system can experience three different types of defects. let ai (i = 1,2,3) denote the event...