




The law of large numbers is a law of probability theory. The mathematical definition of the law of large numbers is that a random sample approaches the expected value of the population as the sample grows. For example, flip a coin ten times and it might come up heads every time. The law of large numbers dictates that if the coin is flipped a million times, the results should be 50/50 heads versus tails. Assuming that investors earn about 7% annually, the law of large numbers suggests that an individual investor will earn that same 7% over time. The law of large numbers can also be applied to earnings growth. It is easier for a company's sales to grow at twenty percent if sales are one million dollars. The law of large numbers states that it is harder to achieve that growth rate if sales are ten billion dollars. The law of large numbers also implies that the probability of a rare event occurring (e.g. winning the lottery) decreases as the number of participants increases.
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