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

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Basic Math

A certain system can experience three different types ofdefects. Let Ai (i = 1,2,3) denote the event that the system has adefect of type i. Suppose that the following probabilities aretrue. P(A1) = 0.10 P(A2) = 0.08 P(A3) = 0.06 P(A1 ? A2) = 0.12 P(A1? A3) = 0.13 P(A2 ? A3) = 0.12 P(A1 ? A2 ? A3) = 0.01 (c) Giventhat the system has at least one type of defect, what is theprobability that it has exactly one type of defect? (Round youranswer to four decimal places.) (d) Given that the system has bothof the first two types of defects, what is the probability that itdoes not have the third type of defect? (Round your answer to fourdecimal places.)

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