# Laplace's formula

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).

## example

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

## literature

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