91Ó°ÊÓ

The emergency backup generators fail 22% of the time whenever needed.

The number of backup generators with the stadium is 3.

An event of at least one occurrence implies that a specific situation occurs once or more than once.The probability of the event is calculated by computing the probability that the event does not occur and then subtracting it from 1.

Mathematically, if A is an event,

$P\left(Aoccurringatleastonce\right)=1-P\left(Anotoccurring\right)$

Let A be the event that a backup generator fails to work.

It has the following probability:

$$\begin{gathered} P\left(A\right)=\frac{22}{100} \\ =0.22 \end{gathered}$$

The probability that among the three generators that all will fail.

$$\begin{gathered} P\left(\text{all}\text{will}\text{fail}\right)=P\left(A\right)×P\left(A\right)×P\left(A\right) \\ =0.22×0.22×0.22 \\ =0.0106 \end{gathered}$$

The probability that out of three generators, at least one will work during a power failure is computed as follows:

$$\begin{gathered} P\left(\text{at}\text{least}\text{one}\text{will}\text{work}\right)=1-P\left(\text{all}\text{will}\text{fail}\right) \\ =1-0.0106 \\ =0.9894 \end{gathered}$$

Therefore, the probability that at least one will work in a power failure out of the three backup generators is 0.989.

The probability that at least one of the three backup generators works during a power failure is relatively high, 0.989 (close to 1).

The probability value seems adequate to fulfill the needs of the stadium during a power failure as it is sufficiently high.