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(A1) 0.14 P(A3) = 0.07 = = P(A2)=0.09 P(A₁ UA2) 0.15 P(A2 A3) 0.13 P(A1 UA3) = 0.17 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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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(A1) 0.14
P(A3) = 0.07
= =
P(A2)=0.09
P(A₁ UA2) 0.15
P(A2 A3) 0.13
P(A1 UA3) = 0.17
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?
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(A1) 0.14 P(A3) = 0.07 = = P(A2)=0.09 P(A₁ UA2) 0.15 P(A2 A3) 0.13 P(A1 UA3) = 0.17 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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