Redundancy in Stadium Generators Large stadiums rely on backup generators to provide electricity in the event of a power failure. Assume that emergency backup generators fail 22% of the times when they are needed (based on data from Arshad Mansoor, senior vice president with the Electric Power Research Institute). A stadium has three backup generators so that power is available if at least one of them works in a power failure. Find the probability of having at least one of the backup generators working given that a power failure has occurred. Does the result appear to be adequate for the stadium’s needs?

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Asked Dec 23, 2019
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Redundancy in Stadium Generators Large stadiums rely on backup generators to provide electricity in the event of a power failure. Assume that emergency backup generators fail 22% of the times when they are needed (based on data from Arshad Mansoor, senior vice president with the Electric Power Research Institute). A stadium has three backup generators so that power is available if at least one of them works in a power failure. Find the probability of having at least one of the backup generators working given that a power failure has occurred. Does the result appear to be adequate for the stadium’s needs?

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Expert Answer

Step 1

From the information, Generators fail is 22%. That is, P (generator fails) = 0.22.

Step 2

The probability of having at least one of the backup generators working given...

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P(At least one generator works ) =1-P(None of them generator works =1-(0.22) =1-0.010648 = 0.9893

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