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.

Question

Ducky

Mathematics

19 September, 06:52

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.

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Irvin Mueller · 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)