Hospitals typically require backup generators to provide electricity in the event of a power outage. 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 hospital has two backup generators so that power is available if one of them fails during a power outage.
a. Find the probability that both generators fail during a power outage.
b. Find the probability of having a working generator in the event of a power outage. Is that probability high enough for the hospital?