posted by Sherry on .
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?
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
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.