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= .13 = .14 O=.10 n A3) = .01 at the system has a type 1 defect, what is the probability that it has a type 2 at the system has a type 1 defect, what is the probability that it has all three e at the system has at least one type of defect, what is the probability that it e type of defect? at the system has both of the first two types of defects, what is the probab have the third type of defect?

= .13 = .14 O=.10 n A3) = .01 at the system has a type 1 defect, what is the probability that it has a type 2 at the system has a type 1 defect, what is the probability that it has all three e at the system has at least one type of defect, what is the probability that it e type of defect? at the system has both of the first two types of defects, what is the probab have the third type of defect?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 2EQ: 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed...
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A certain system can experience three different types of defects. Let Ai (i = 1,2,3) denote the event that the system has a defect of type i. Suppose that P(A1) = .12 P(A2) = .07 P(A3) = .05 P(A1 U A2) = .13 P(A1 U A3) = 14 P(A2 U A3) = 10 P(A1n A2 n A3) = .01 a. Given that the system has a type 1 defect, what is the probability that it has a type 2 defect? b. Given that the system has a type 1 defect, what is the probability that it has all three types of defects? c. Given that the system has at least one type of defect, what is the probability that it has exactly one type of defect? 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?
Transcribed Image Text:A certain system can experience three different types of defects. Let Ai (i = 1,2,3) denote the event that the system has a defect of type i. Suppose that P(A1) = .12 P(A2) = .07 P(A3) = .05 P(A1 U A2) = .13 P(A1 U A3) = 14 P(A2 U A3) = 10 P(A1n A2 n A3) = .01 a. Given that the system has a type 1 defect, what is the probability that it has a type 2 defect? b. Given that the system has a type 1 defect, what is the probability that it has all three types of defects? c. Given that the system has at least one type of defect, what is the probability that it has exactly one type of defect? 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?
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