Equally likely outcomes
There are some kinds of experiment where we believe that all possible outcomes have the same chance of arising. This is usually justified by symmetry in the physical mechanism underlying the experiment. For example,
Definition
If an experiment has \(N\) equally likely outcomes and an event, \(E\), consists of \(x\) of them, then its probability is defined to be
\[P(E) = \frac x N\]In other words,
\[P(event) = \frac {\text{Number of outcomes in } event} {\text{Number of outcomes in sample space}}\]This is called the classical definition of probability and is the easiest to understand.
Sampling a value from a finite population
Many applications with equally likely outcomes involve games of chance such as cards, dice and roulette wheels.
However equally likely outcomes also arise when sampling a value from a finite population. If all population members have the same chance of selection, then this definition of probability can again be used.
Household size in Mauritius
The following bar chart describes the size of all households in Mauritius in its 2011 census.
The probability that a randomly chosen household is of any size is the proportion of such households in the census.