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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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Statistics

A certain system can experience three different types ofdefects. Let Ai (i = 1,2,3) denote theevent that the system has a defect of type i. Suppose thatthe following probabilities are true.

P(A1) =0.10      P(A2)=0.07     P(A3)= 0.05
P(A1 ∪ A2) =0.11      P(A1∪ A3) = 0.12
P(A2 ∪ A3) =0.10      P(A1∩ A2 ∩ A3) = 0.01

(a) Given that the system has a type 1 defect, what is theprobability that it has a type 2 defect? (Round your answer to fourdecimal places.)


(b) Given that the system has a type 1 defect, what is theprobability that it has all three types of defects? (Round youranswer to four decimal places.)


(c) Given that the system has at least one type of defect, what isthe probability that it has exactly one type of defect? (Round youranswer to four decimal places.)


(d) Given that the system has both of the first two types ofdefects, what is the probability that it does not have the thirdtype of defect? (Round your answer to four decimal places.)

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