Posted by Sherry on Saturday, July 14, 2012 at 9:15pm.
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?

statistics  MathMate, Sunday, July 15, 2012 at 6:15pm
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 (10.05)=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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