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The gory math...
If 99% of the population is not armed, then the probability of any one person randomly selected from the population being not armed is .99. If you draw a random sample of 2, the probability that both are not armed is .99^2. If you draw a random sample of 3, the probability that all 3 are not armed is .99^3.
So the probability of everyone in a random group of 100 being not armed is .99^100.
1 minus that number is the probability of having at least 1 gun in the group of 100.
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