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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) = 0.11 P(A₂) = 0.08 P(A3) = 0.06 P(A₁ U A3) = 0.14 P(A₁ U A₂) = 0.13 P(A₂ U A3) = 0.12 P(A1 A₂ A3) = 0.01 (a) Given that the system has a type 1 defect, what is the probability that it has a type 2 defect? (Round your answer to four decimal places.) (b) Given that the system has a type 1 defect, what is the probability that it has all three types of defects? (Round your answer to four decimal places.) (c) Given that the system has at least one type of defect, what is the probability that it has exactly one type of defect? (Round your answer to four decimal places.) (d) Given that the system has both of the first two types of defects, what is the probability that it does not have the third type of defect? (Round your answer to four decimal places.)

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) = 0.11 P(A₂) = 0.08 P(A3) = 0.06 P(A₁ U A3) = 0.14 P(A₁ U A₂) = 0.13 P(A₂ U A3) = 0.12 P(A1 A₂ A3) = 0.01 (a) Given that the system has a type 1 defect, what is the probability that it has a type 2 defect? (Round your answer to four decimal places.) (b) Given that the system has a type 1 defect, what is the probability that it has all three types of defects? (Round your answer to four decimal places.) (c) Given that the system has at least one type of defect, what is the probability that it has exactly one type of defect? (Round your answer to four decimal places.) (d) Given that the system has both of the first two types of defects, what is the probability that it does not have the third type of defect? (Round your answer to four decimal places.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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) = 0.08 P(A3) = 0.06 P(A₁) = 0.11 P(A1 U A₂) = 0.13 P(A1 U A3) = 0.14 P(A₂ U A3) = 0.12 P(A₁ A₂ A3) = 0.01 (a) Given that the system has a type 1 defect, what is the probability that it has a type 2 defect? (Round your answer to four decimal places.) (b) Given that the system has a type 1 defect, what is the probability that it has all three types defects? (Round your answer to four decimal places.) (c) Given that the system has at least one type of defect, what is the probability that it has exactly one type of defect? (Round your answer to four decimal places.) (d) Given that the system has both of the first two types of defects, what is the probability that it does not have the third type of defect? (Round your answer to four decimal places.)
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) = 0.08 P(A3) = 0.06 P(A₁) = 0.11 P(A1 U A₂) = 0.13 P(A1 U A3) = 0.14 P(A₂ U A3) = 0.12 P(A₁ A₂ A3) = 0.01 (a) Given that the system has a type 1 defect, what is the probability that it has a type 2 defect? (Round your answer to four decimal places.) (b) Given that the system has a type 1 defect, what is the probability that it has all three types defects? (Round your answer to four decimal places.) (c) Given that the system has at least one type of defect, what is the probability that it has exactly one type of defect? (Round your answer to four decimal places.) (d) Given that the system has both of the first two types of defects, what is the probability that it does not have the third type of defect? (Round your answer to four decimal places.)
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