Question

Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail

3131​%

of the times when they are needed. A hospital has two backup generators so that power is available if one of them fails during a power outage. Complete parts​ (a) and​ (b) below.

a. Find the probability that both generators fail during a power outage.

0.09610.0961

​(Round to four decimal places as​ needed.)

b. Find the probability of having a working generator in the event of a power outage. Is that probability high enough for the​ hospital? Assume the hospital needs both generators to fail less than​ 1% of the time when needed.

0.90390.9039

​(Round to four decimal places as​ needed.)

Is that probability high enough for the​ hospital? Select the correct answer below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

​Yes, because both generators fail about

nothing ​%

of the time they are​ needed, which is low enough to not impact the health of patients.

​(Round to the nearest whole number as​ needed.)

B.

​Yes, because it is impossible for both generators to fail.

C.

​No, because both generators fail about

nothing ​%

of the time they are needed. Given the importance of the​ hospital's needs, the reliability should be improved.

​(Round to the nearest whole number as​ needed.)

Answer 1