Question

Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 37​% 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. ????​(Round to four decimal places as​ needed.)

Answer 1

SOLUTION:

From given data,

Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 37​% 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.

The probability of an event can be defined as follows:

Probability = Number of outcomes in favor of the event / Total number of outcomes in the sample space.

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

The probability that both generators fail during a power outage is

P(Generator fail) = 37% = 37/100 = 0.37

Since generators are independent so the probability that both generator fail during a power outage is,

P(Both Generator fail) = P(Generator fail) * P(Generator fail)

P(Both Generator fail) = 0.37 * 0.37

P(Both Generator fail) = 0.1369

Hence, required probability is 0.1369