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

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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) =
0.10      P(A2)
=
0.08     P(A3)
= 0.05
P(A1 ∪ A2) =
0.12      P(A1
∪ A3) = 0.12
P(A2 ∪ A3) =
0.11      P(A1
∩ A2 ∩ A3) = 0.01
(a) Given that the system has a type 1 defect, what is the
probability that it has a type 2 defect? (Round your answer to four
decimal places.)


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


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


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