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Module by: Paul E Pfeiffer. E-mail the author

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Name: Likelihood
ID: m23243
Language: English (en)
Summary: Early developments of probability as a mathematical discipline came as a response to questions about games of chance played repeatedly. The mathematical formulation owes much to the work of Pierre de Fermat and Blaise Pascal in the seventeenth century. The game is described in terms of a well defined trial (a play); the result of any trial is one of a specific set of distinguishable outcomes. Although the result of any play is not predictable, certain “statistical regularities” of results are observed. In classical probability, the possible results are described in ways that make each result seem equally likely. If there are N such possible “equally likely” results, each is assigned a probability 1/N. The developers of mathematical probability also took cues from early work on the analysis of statistical data. To apply these results, one considers the selection of a member of the population on a chance basis. One then assigns the probability that such a person will have a given condition. The trial here is the selection of a person, but the interest is in the condition. Out of this statistical formulation came an interest not only in probabilities as fractions or relative frequencies but also in averages or expectatons. These averages play an essential role in modern probability. This approach avoided the "equally likely" limitation of classical probability. Inherent in informal thought, as well as in precise analysis, is the notion of an event to which a probability may be assigned as a measure of the likelihood the event will occur will occur on any trial. A successful mathematical model must formulate these notions with precision. The event corresponding to some characteristic of the possible outcomes is the set of those outcomes having this characteristic. The event occurs if and only if the outcome of the trial is a member of that set (i.e., has the characteristic determining the event).
Subject: Mathematics and Statistics
Keywords: DeMorgan's rules, Disjoint unions, Events as sets, Indicator functions, Logical operations, Mutually exclusive, Outcomes, Set inclusion, Venn diagrams
License: Creative Commons Attribution License CC-BY 3.0

Authors: Paul E Pfeiffer (
Copyright Holders: Paul E Pfeiffer (
Maintainers: Paul E Pfeiffer (, Daniel Williamson (, C. Sidney Burrus (

Latest version: 1.8 (history)
First publication date: Apr 13, 2009 3:15 pm -0500
Last revision to module: Sep 18, 2009 1:11 pm -0500


PDF: m23243_1.8.pdf PDF file, for viewing content offline and printing. Learn more.
XML: m23243_1.8.cnxml XML that defines the structure and contents of the module, minus any included media files. Can be reimported in the editing interface. Learn more.

Version History

Version: 1.8 Sep 18, 2009 1:11 pm -0500 by Daniel Williamson
added google analytics tracking code

Version: 1.7 Aug 3, 2009 4:11 pm -0500 by Paul E Pfeiffer
Big V for disjoint union

Version: 1.6 Jul 27, 2009 12:06 pm -0500 by Daniel Williamson
disjoint union fix

Version: 1.5 Jun 19, 2009 11:10 am -0500 by Daniel Williamson
m-file fixes, supplemental links, metadata updated

Version: 1.4 Jun 9, 2009 5:17 pm -0500 by Daniel Williamson
updated links, images and accessibility

Version: 1.3 May 26, 2009 4:32 pm -0500 by Daniel Williamson
fixed module names, and updated content structure

Version: 1.2 May 13, 2009 4:37 pm -0500 by Paul E Pfeiffer

Version: 1.1 May 13, 2009 11:14 am -0500 by Paul E Pfeiffer

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