# statistics

The probability that a house is burglarized in the city is 5%. If 50 houses are randomly selected, what is the probability that none will be burglarized?

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1. Assuming a large city (so that the sample size does not affect the population probability), then the probability of a house is NOT burglarized is (1-0.05)=0.95.

By the multiplication law, randomly selecting 50 houses not burglarized is
P(50)=0.95^50=0.077.

If you work the other way round, and look for randomly selecting 50 houses ALL burglarized, the probability of that happening is then
P(50)=0.05^50=8.9*10^(-66), very small indeed.

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