Browse Definitions :
Definition

law of large numbers

Contributor(s): Stan Gibilisco

The law of large numbers is a principle of probability according to which the frequencies of events with the same likelihood of occurrence even out, given enough trials or instances. As the number of experiments increases, the actual ratio of outcomes will converge on the theoretical, or expected, ratio of outcomes.

For example, if a fair coin (where heads and tails come up equally often) is tossed 1,000,000 times, about half of the tosses will come up heads, and half will come up tails. The heads-to-tails ratio will be extremely close to 1:1. However, if the same coin is tossed only 10 times, the ratio will likely not be 1:1, and in fact might come out far different, say 3:7 or even 0:10.

The law of large numbers is sometimes referred to as the law of averages and generalized, mistakenly, to situations with too few trials or instances to illustrate the law of large numbers. This error in logic is known as the gambler’s fallacy.

If, for example, someone tosses a fair coin and gets several heads in a row, that person might think that the next toss is more likely to come up tails than heads because they expect frequencies of outcomes to become equal. But, because each coin toss is an independent event, the true probabilities of the two outcomes are still equal for the next coin toss and any coin toss that might follow.

Nevertheless, if the coin is tossed enough times, because the probability of the either outcome is the same, the law of large numbers comes into play and the number of heads and tails will be close to equal.

This was last updated in December 2012

Continue Reading About law of large numbers

Join the conversation

1 comment

Send me notifications when other members comment.

Please create a username to comment.

The last paragraph isn't quite right. The difference between the number of heads and the of tails tends to diverge.  It's the frequency, that is, the fraction of heads that approaches a constant, 0.5 for a fair coin.
Cancel

-ADS BY GOOGLE

File Extensions and File Formats

Powered by:

SearchCompliance

  • compliance audit

    A compliance audit is a comprehensive review of an organization's adherence to regulatory guidelines.

  • regulatory compliance

    Regulatory compliance is an organization's adherence to laws, regulations, guidelines and specifications relevant to its business...

  • Whistleblower Protection Act

    The Whistleblower Protection Act of 1989 is a law that protects federal government employees in the United States from ...

SearchSecurity

  • brute force attack

    Brute force (also known as brute force cracking) is a trial and error method used by application programs to decode encrypted ...

  • spyware

    Spyware is software that is installed on a computing device without the user's knowledge. Spyware can be difficult to detect; ...

  • ATM black box attack

    An ATM black box attack, also referred to as jackpotting, is a type of banking-system crime in which the perpetrators bore holes ...

SearchHealthIT

SearchDisasterRecovery

  • business continuity and disaster recovery (BCDR)

    Business continuity and disaster recovery (BCDR) are closely related practices that describe an organization's preparation for ...

  • warm site

    A warm site is a type of facility an organization uses to recover its technology infrastructure when its primary data center goes...

  • disaster recovery (DR) test

    A disaster recovery test (DR test) is the examination of each step in a disaster recovery plan as outlined in an organization's ...

SearchStorage

  • enterprise storage

    Enterprise storage is a centralized repository for business information that provides common data management, protection and data...

  • disk array

    A disk array, also called a storage array, is a data storage system used for block-based storage, file-based storage or object ...

  • optical storage

    Optical storage is any storage type in which data is written and read with a laser. Typically, data is written to optical media, ...

Close