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A certain system can experience three different types of defects. Let Ai (i = 1,2,3) denote...

A certain 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) = 0.16      P(A2) = 0.10     P(A3) = 0.08
P(A1 ∪ A2) = 0.18      P(A1 ∪ A3) = 0.19
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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