Question

Consider the system of components connected as in the accompanying picture. Components 1 and 2 are connected in parallel, so that subsystem works iff either 1 or 2 works; since 3 and 4 are connected in series, that subsystem works iff both 3 and 4 work. If components work independently of one another and P(component i works) = .9 for i = 1,2 and = .8 for i = 3,4, calculate P(system works).

Name: Consider the system of components connected as in the accompanying picture. Components 1 and 2 are connected in parallel, so that subsystem works iff either 1 or 2 works; since 3 and 4 are connected in series, that subsystem works iff both 3 and 4 work. If components work independently of one another and P(component i works) = .9 for i = 1,2 and = .8 for i = 3,4, calculate P(system works).
Uploaded: 2022-01-27T22:30:36-08:00
Duration: 4 min 19 s
Channel: Robin Corrigan
Description: Consider the system of components connected as in the accompanying picture. Components 1 and 2 are connected in parallel, so that subsystem works iff either 1 or 2 works; since 3 and 4 are connected in series, that subsystem works iff both 3 and 4 work. If components work independently of one another and P(component i works) = .9 for i = 1,2 and = .8 for i = 3,4, calculate P(system works).

          Consider the system of components connected as in the accompanying picture. Components 1 and 2 are connected in parallel, so that subsystem works iff either 1 or 2 works; since 3 and 4 are connected in series, that subsystem works iff both 3 and 4 work. If components work independently of one another and P(component i works) = .9 for i = 1,2 and = .8 for i = 3,4, calculate P(system works).

Consider the system of components connected as in the accompanying picture. Components 1 and 2 are connected in parallel, so that subsystem works iff either 1 or 2 works; since 3 and 4 are connected in series, that subsystem works iff both 3 and 4 work. If components work independently of one another and P(component i works) = .9 for i = 1,2 and = .8 for i = 3,4, calculate P(system works).

Added by Jessica R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Robin Corrigan

01/27/2022

Step 1

The parallel subsystem works if either component 1 or component 2 works. The probability that a single component fails is: \[ P(\text{component 1 fails}) = 1 - P(\text{component 1 works}) = 1 - 0.9 = 0.1 \] \[ P(\text{component 2 fails}) = 1 - P(\text{component Show more…

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Consider the system of components connected as in the accompanying picture. Components 1 and 2 are connected in parallel, so that subsystem works iff either 1 or 2 works; since 3 and 4 are connected in series, that subsystem works iff both 3 and 4 work. If components work independently of one another and P(component i works) = .9 for i = 1,2 and = .8 for i = 3,4, calculate P(system works).