The Law of Large Numbers
reprinted with permission by Philip Stark, Ph.D. (University of California at Berkeley)

The Law of Large Numbers says that in repeated, independent trials with the same probability p of success in each trial, the percentage of successes is increasingly likely to be close to the chance of success as the number of trials increases.   More precisely, the chance that the percentage of successes differs from the probability p by more than a fixed positive amount, e > 0, converges to zero as the number of trials n goes to infinity, for every number e > 0. Note that in contrast to the difference between the percentage of successes and the probability of success, the difference between the number of successes and the expected number of successes, n×p, tends to grow as n grows.