Laplace's formula

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The Laplace formula is a mathematical formula from the elementary theory of probability . If a random experiment only has a finite number of results and they all have the same probability , then the following applies to the probability of an event :

or more formal


if and denote the number of elements of the event or result set .

The formula is named after the French mathematician and astronomer Pierre Simon Laplace (1749–1827).


When throwing a dice twice, there are 36 possible outcomes for the number combinations


If there are four results, the total is 9, namely at (6, 3), (5, 4), (4, 5), (3, 6). The probability of the event to get the sum 9 is thus given by


See also


  • Ulrich Krengel: Introduction to probability theory and statistics . For studies, professional practice and teaching. 8th edition. Vieweg, Wiesbaden 2005, ISBN 3-8348-0063-5 .