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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(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, UA3) = 0.17 P(A, n A, 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?

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, UA3) = 0.17 P(A, n A, 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?

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
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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(A,) = P(A, U A2) = 0.16 P(A2 U A3) = 0.12 = 0.15 P(A2) = 0.09 P(A3) = 0.06 P(A, U A3) = 0.17 P(A1 n Az 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(A,) = P(A, U A2) = 0.16 P(A2 U A3) = 0.12 = 0.15 P(A2) = 0.09 P(A3) = 0.06 P(A, U A3) = 0.17 P(A1 n Az 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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