A rainstorm in Portland, Oregon, has wiped out the electricity in about 10% 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. Round your response to at least three decimal places.

Answer:There is a 53.14% probability that none of them has lost electricity in his/her household.Step-by-step explanation:For each of the households, there are only two possible outcomes. Either they lost electricity, or they did not. This means that we can solve this problem using concepts of the binomial probability distribution.Binomial probability distributionThe binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]In which [tex]C_{n,x}[/tex] is the number of different combinatios of x objects from a set of n elements, given by the following formula.[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]And [tex]p[/tex] is the probability of X happening.In this problem we have that:A success is a household losing electricity, so [tex]p = 0.1[/tex].The team has 6 members, so [tex]n = 6[/tex].What is the probability that none of them has lost electricity in his/her household?This is P(X = 0).[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex][tex]P(X = 0) = C_{6,0}.(0.10)^{0}.(0.9)^{6} = 0.5314[/tex]There is a 53.14% probability that none of them has lost electricity in his/her household.