Let *p* be the mathematical probability of success and *k/N* be the actual success ratio. The question is how close is *k/N* to *p*? In modern notation, where ε represents any small positive number chosen,

converges to 1, as *N* grows large.

Using Chebyshev’s inequality and some simple algebra, we may prove the theorem. If we perform a binomial experiment *N* times, then (by definition of the probability) the expected ...

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