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What's Luck Got to Do with It? by Joseph Mazur

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The Weak Law of Large Numbers

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,

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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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