A certain system can experience three different types of defects. Let A; (i = 1,2,3) denote the event that the system has a defect of type i. Suppose that the following probabilities are true. P(A3) = 0.07 P(A1) = 0.16 P(A2) = 0.10 P(A1 U A3) = 0.18 P(A1 U A2) = 0.18 P(A2 U A3) = 0.14 P(A1 N A2 N 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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A certain system can experience three different types of defects. Let A; (i = 1,2,3) denote the event that the system has a defect of type i. Suppose that the following probabilities are true.
P(A3) = 0.07
P(A1) = 0.16
P(A2) = 0.10
P(A1 U A3) = 0.18
P(A1 U A2) = 0.18
P(A2 U A3) = 0.14
P(A1 N A2 N 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?
Transcribed Image Text:A certain system can experience three different types of defects. Let A; (i = 1,2,3) denote the event that the system has a defect of type i. Suppose that the following probabilities are true. P(A3) = 0.07 P(A1) = 0.16 P(A2) = 0.10 P(A1 U A3) = 0.18 P(A1 U A2) = 0.18 P(A2 U A3) = 0.14 P(A1 N A2 N 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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