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Law of large numbers

A compact thinking tool for spotting patterns and avoiding mistakes.

  1. The useful idea

    In probability theory, the law of large numbers is a mathematical law which states that the average of the results obtained from a large number of independent random samples converges to the true value,

  2. How it works

    More formally, the law of large numbers states that given a sample of independent and identically distributed values, the sample mean converges to the true mean.

  3. Why it matters

    The law of large numbers is important because it guarantees stable long-term results for the averages of some random events.

Use Law of large numbers as a quick check before trusting your first conclusion.

Use Law of large numbers as a quick check before trusting your first conclusion.

Test your recall

Which idea belongs to the explanation of Law of large numbers?

  • The useful idea — correct
  • How it works
  • Why it matters

In probability theory, the law of large numbers is a mathematical law which states that the average of the results obtained from a large number of independent random samples converges to the true value,

EvergreenLast verified 2026-07-19

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