A hospital is to be supplied with reliable electric power Th

A hospital is to be supplied with reliable electric power. The municipal power company can supply power with a probability of failure of 0.03. A back-up system is to be added to the facility to bring the power supply reliability to value of 0.999. Determine the probability of failure of the back-up power supply.

Solution

The municipal power company can supply power with a probability of failure of 0.03.

Consider, this as P(A) = 0.03

A back-up system is to be added to the facility to bring the power supply reliability to value of 0.999.

P(B) = 1 - 0.999 = 0.001.............................( It is probability for failure of back system)

These are two independent events.

Therefore,

P[of failure of the back-up power supply.] = P(A)*P(B) = 0.03 *0.001 = 0.00003