Math Problem Statement
Consider the system of components connected as in the accompanying picture. Components 1 and 2 are connected in parallel, so that subsystem works if and only if either 1 or 2 works; since 3 and 4 are connected in series, that subsystem works if and only if both 3 and 4 work. If components work independently of one another and P(component i works) = 0.86 for i = 1, 2 and = 0.75 for i = 3, 4, calculate P(system works). (Round your answer to four decimal places.)
Solution
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Math Problem Analysis
Mathematical Concepts
Probability Theory
Series and Parallel Systems
Independent Events
Formulas
P(Parallel subsystem works) = 1 - P(both fail)
P(Series subsystem works) = P(Component 3 works) × P(Component 4 works)
P(System works) = P(Parallel subsystem works) × P(Series subsystem works)
Theorems
Multiplication rule for independent events
Probability of failure for parallel components
Product rule for series components
Suitable Grade Level
Undergraduate level
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