law of large numbers

American  

noun

Mathematics.

1. the theorem in probability theory that the number of successes increases as the number of experiments increases and approximates the probability times the number of experiments for a large number of experiments.

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law of large numbers British  

noun

1. the fundamental statistical result that the average of a sequence of n identically distributed independent random variables tends to their common mean as n tends to infinity, whence the frequency of the occurrence of an event in n independent repetitions of an experiment tends to its probability

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law of large numbers Scientific  

1. The rule or theorem that the average of a large number of independent measurements of a random quantity tends toward the theoretical average of that quantity.

2. Also called Bernoulli's law

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Etymology

Origin of law of large numbers

First recorded in 1935–40

Example Sentences

“By the time these companies go public, the law of large numbers kicks in.”

From Barron's • May 21, 2026

But its shares fell in extended trading, which Ruth Foxe-Blader, managing partner at US venture capital firm Citrine Venture Partners, put down to "a law of large numbers".

From BBC • May 21, 2026

The law of large numbers hasn’t seemed to catch up to Nvidia yet.

From The Wall Street Journal • Nov. 20, 2025

The law of large numbers states that the larger the sample size you take from a population, the closer the sample mean, x¯ , gets to μ.

From Textbooks • Mar. 27, 2020

And contrary to countless barroom conversations, the law of large numbers doesn’t imply the gambler’s fallacy: that a head is more likely after a string of tails.

From "Innumeracy: Mathematical Illiteracy and Its Consequences" by John Allen Paulos