Hospitals typically require backup generators to provide electricity in the even
ID: 3376698 • Letter: H
Question
Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 25% 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. 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 enoigh for the hospital? Assume the hospitak needs both generators to fail less than 1% of the time when needed. C) Is that probability high enough for the hospital?
Explanation / Answer
Probability that a generator fails when needed = 25% = 0.25
A) Probability that both generators fail during a power outage = 0.25*0.25 = 0.0625
B) Probability of having a working generator = P(both generator work) + 2*P(one generator works) = 0.75*0.75 + 0.25*0.75 = 0.9375
(c) No, as the probability required is 99%, the probability of 0.9375 is not high enough for the hospital.
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