Cardinalities in proofreading

In 1975, G. Pólya suggested that if two proofreaders found $a$ and $b$ errors in a text, of which $c$ errors were found by both of them, then a reasonable approximation of the unknown number $e$ of all errors is $e\approx ab\mathrm{/}c$. We justify this formula by constructing a realistic model of proofreaders and estimating the efficiency of this model with the help of the bound on large deviations in the Probabilistic Method. In conclusion we discuss the distinction between realistic and probabilistic models of problems.