The rule of three states that if a certain event did not occur in a sample with n subjects, the interval from 0 to 3/n is a 95% confidence interval for the rate of occurrences in the population. When n is greater than 30, this is a good approximation of results from more sensitive tests.
Source: https://en.wikipedia.org/wiki/Rule_of_three_(statistics)
A citation for this is Ernst, et al., 1995.
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