Question

A rainstorm in Portland, Oregon, has wiped out the electricity in about 5% of the households in the city. A management team in Portland has a big meeting tomorrow, and all 6 members of the team are hard at work in their separate households, preparing their presentations. What is the probability that none of them has lost electricity in his/her household? Assume that their locations are spread out so that loss of electricity is independent among their households.

Answer 1

Binomial distribution because:
Trials are Bernoulli (affected or not)
Probability is known (p=0.05) and remains constant for all trials.
Number of trials is known (n=6).

P(x)=C(n,x)p^x*(1-p)^(n-x)

x=0 =>
P(0)=C(6,0)(0.05^0)(0.95^6)
=0.7351.... (approximately)