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4-23 The guidance system design of a satellite places several components in parallel. The system will function as long as at least one of the components is operational. In a particular satellite, 4 such components are placed in parallel. If the probability of a component operating successfully is 0.9, what is the probability of the system functioning? What is the probability of the system failing? Assume that the components operate independently of each other.

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Answer #1

Question 4.23

Here the components operate independently of each other.

Here probability of each component operating seperately = 0.9

and there are four such components in parellal. Here in parellal system if all of the compnents fail then only the system will stop functioning.

So we first evaluate the probability of the system failing = Pr(Comp 1 Fail) * Pr(Comp 2 fail) * Pr(comp3 fail) * Pr(Comp 4 fail)

= 0.14 = 0.0001

Here probaability that system will work =1 - Pr(Sysem will fail) = 1 - 0.0001 = 0.9999

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