## Related questions with answers

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?

Solution

VerifiedGive probability:

$\begin{equation*} P(\text{ a generator fails }|\text{ it is needed })=0.22 \end{equation*}$

There are three backup generators, one is needed if the other two have failed

The exercise is to compute $P(\textit{ at least one backup generator works })$, this will be done by applying $\textbf{\textcolor{#4257b2}{the rule of the complement}}$ and $\textbf{\textcolor{#c34632}{the multiplication rule}}$

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