The power supply to a hospital operating room may come from electricity (E) or a

Question

The power supply to a hospital operating room may come from electricity (E) or a diesel generator (D). The diesel generator starts operating only if there is no electricity. The probability that there will be no electricity at any given time is 0.001. If the diesel generator has to supply the power, the probability that it will fail is 0.01. (a)What is the probability that there will be no power in the operating room? (b)If there is power in the operating room, what is the probability that both sources of power are in good operating condition?

Explanation / Answer

Let

E = electricity works
D = diesel works
P = there is power

a)

P(D' n E') = P(E') P(D'|E') = 0.001*0.01 = 0.00001 [ANSWER]

********************

b)

If the event in part A does not happen, there is power. Hence,

P(P) = 1 - 0.00001 = 0.99999

Hence,

P(D n E|P) = P(E) P(D)/P(P) = (1-0.001)*(1-0.01)/0.99999 = 0.98901989 [ANSWER]

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.