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(A,) = 0.15 P(A, U A2) = 0.16 P(A, U A3) = 0.12 P(A2) = 0.09 P(A3) = 0.06 P(A, U Ag) = 0.17 P(A, n Az n Ag) = 0.02 (a).What.is.the probability that the system does not have a type 1 defect? Enter a number. (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?
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(A,) = 0.15 P(A, U A2) = 0.16 P(A, U A3) = 0.12 P(A2) = 0.09 P(A3) = 0.06 P(A, U Ag) = 0.17 P(A, n Az n Ag) = 0.02 (a).What.is.the probability that the system does not have a type 1 defect? Enter a number. (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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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(A,) = 0.15
P(A, U A2) = 0.16
P(A2 U A3) = 0.12
P(A2) = 0.09
P(A, U A3) = 0.17
P(A, n A2 n A3) = 0.02
P(A,) = 0.06
.(a).What.is.the probability that the system does not have a type 1 defect?
Enter a number.
(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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In the provided information, it can be interpreted that the probability types of the defects, i.e., type-1, type-2, and type-3 are denoted by, P(A1), P(A2), and P(A3). Furthermore, it can be claimed that the events, i.e., the type-1, type-2, and type-3 defects are not disjoint.
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