Mostly because I thought it was fun, a worked example where you mark 100 different flies and then catch 100 unmarked flies (releasing each fly individually immediately after catching it; maybe you caught the same fly 100 times):
By the rule of three, we estimate the probability that a fly in your house is marked at p < 3/100.
We can also model the probability that a fly in your house is marked as 100/n, where n is the number of flies in your house.
Then 100/n < 3/100 and n > 100*100/3 = 3,333. There are probably more than 3333 flies in your house.
By the rule of three, we estimate the probability that a fly in your house is marked at p < 3/100.
We can also model the probability that a fly in your house is marked as 100/n, where n is the number of flies in your house.
Then 100/n < 3/100 and n > 100*100/3 = 3,333. There are probably more than 3333 flies in your house.