An Introduction to Mathematical Statistics and Its Applications (6th Edition)

Published by Pearson
ISBN 10: 0-13411-421-3
ISBN 13: 978-0-13411-421-7

Chapter 2 Probability - 2.2 Sample Spaces and the Algebra of Sets - Questions - Page 22: 19

Answer

$A=(A₁₁∩A₂₁)∪(A₂₁∩A₂₂)$

Work Step by Step

The first subsystem will fail if both components fail, which is represented by: A₁₁∩A₂₁ The second subsystem will fail if both components fail, which is represented by: A₂₁∩A₂₂ The system will fail if at least one of the subsystems fail, which is represented by $A=(A₁₁∩A₂₁)∪(A₂₁∩A₂₂)$
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