Laplace probability

Experiments in which all results are equally likely are called Laplace experiments.

Remember

With $n$ possible results in a Laplace experiment, each has the probability $\frac{ 1 }{ n }$.

The probability of an event is calculated in a Laplace experiment with the formula:

$P(E) = \frac{|E|}{|\Omega|}$

$|E| ...$ Number of results where $E$ occurs
$|\Omega| ...$ Total number of results

Examples

Examples of Laplace experiments are the throwing of a coin, a dice or the turning of a wheel of fortune with fields of equal size.

A dice is thrown. Your are interested in the probability of an even number.

Sample space: $\Omega=\{1,2,3,4,5,6\}$

Event: $E=\{2, 4, 6\}$

Probability: $P(E) = \frac{|E|}{|\Omega|}$ $=\frac{3}{6}$

Non-Laplace experiment

In non-Laplace experiments, the probabilities for each possible outcome can not be determined by e.g. symmetry considerations or the like. However, after many experiments have been carried out, estimates of the probabilities can be determined.

Examples

Examples of non-Laplace experiments are the throwing of thumbtacks, a LEGO stone or a crown cork. It is not exactly possible to say which event occurs with which probability.