Proofreading Mistakes

If proofreader  finds  mistakes and proofreader  finds  mistakes,  of which were also found by , how many mistakes were missed by both  and ? Assume there are a total of  mistakes, so proofreader  finds a fraction  of all mistakes, and also a fraction  of the mistakes found by . Assuming these fractions are the same, then solving for  gives

The number of mistakes missed by both is therefore approximately

REFERENCES:

Pólya, G. "Probabilities in Proofreading." Amer. Math. Monthly, 83, 42, 1976.