A small college town is supplied electricity by a company. The company has 10 di
ID: 3276144 • Letter: A
Question
A small college town is supplied electricity by a company. The company has 10 different power generators supplying electricity to the town. Power plant i fails with probability pi independently for different power plants (so one power plant failing does not affect the probability of another power plant failing).
Assume that any one power generator produces enough power to supply the entire town. What is the probability that the town has a blackout? Here pi are some fixed numbers between 0 and 1. Your answer will be a formula in terms of the pi's.
Explanation / Answer
Given:- n= 10 =i
We assume the value of pi= 0.6
Suppose the power plant fails with probability 0.6.
We use two power plant because one power plant failing does not affect the probability of another power plant failing.
We use binomial probability distribution function
= P(i fails) + P (1-i fails)
= P(10 fails) + P(9 fails)
= 10C10 * (pi) 10 * (1-pi)10-10 + 10C9 *(pi)9 * (1-pi)10-9
= 1*(0.6)10 *(0.4)0 + 10*(0.6)9*(0.4)1
= 0.006046 + 0.040308
= 0.046354 = 0.047 rounded value