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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(A₂) = 0.15 P(A₂) = 0.11 P(A3) = 0.09 P(A₂UA₂) = 0.18 P(A₂ UA3) = 0.19 P(A₂ UA3) = 0.16 (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? P(A₁ A₂ A3) = 0.02 (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? Need Help? Read It Watch It

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(A₂) = 0.15 P(A₂) = 0.11 P(A3) = 0.09 P(A₂UA₂) = 0.18 P(A₂ UA3) = 0.19 P(A₂ UA3) = 0.16 (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? P(A₁ A₂ A3) = 0.02 (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? Need Help? Read It Watch It

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.5: Markov Chain
Problem 15E: Smokers and Non smokers In a population of 10,000, there are 5000 non-smokers, 2500 smokers of one...
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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(A₂) = 0.15 P(A₂) = 0.11 P(A3) = 0.09 P(A₁ UA₂) = 0.18 P(A₁ UA3) = 0.19 P(A₂ UA3) = 0.16 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? Need Help? Read It Watch It
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(A₂) = 0.15 P(A₂) = 0.11 P(A3) = 0.09 P(A₁ UA₂) = 0.18 P(A₁ UA3) = 0.19 P(A₂ UA3) = 0.16 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? Need Help? Read It Watch It
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