Question

One percent of faults occurring in a highly available system need the actual repair or replacement of the components, while the remaining 99% are cleared by reboot. Find the probability that among a sample of 200 faults, there are no faults that require calling the repair person. Compute the probability using:

a) Binomial distribution

b) Poisson approximation to the Binomial distribution.

Answer 1

a)
probability that a repair person to be called, p = 0.01
n = 200

Probability that no faults require calling the repair person = (1 - 0.01)^200 = 0.1340

b)
for Poisson approximation to the Binomial distribution
lambda = np = 200*0.01 = 2

P(X = x) = lambda^x * e^(-lambda)/x!

P(X = 0) = 2^0 * e^(-2)/0!

P(X = 0) = 0.1353