Hospitals typically require backup generators to provide electricity in the even

Question

Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 4343% 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

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.

Explanation / Answer

here probability of failing a generator =0.43 ( please revert as abvoe figure seems redundant and if it is 4.3% or 43% , I am considering that to be 43%)

a)probability that both generators fail during a power outage =0.43*0.43 =0.1849

b)probability of having a working generator in the event of a power outage =1-P(both generators fail) =1-0.1849

=0.8151

here as probability of both generators to fail 9s 0.1849 (18.49%) which is greater then 1% ; therefore above probability is not  high enough for the hospital

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