# Definition:Probability

## Probability

### Informal Definition

The **probability** of an event is the likelihood that the event will occur (within a certain formally or informally understood context).

As such, a **probability** can range from $0$ (will never happen) to $1$ (is certain to happen).

Commonly, a **probability** is often stated in terms of a percentage.

### Formal Definition

Let $\EE$ be an experiment.

Let $A \in \Sigma$ be an event in the event space $\Sigma$ of $\EE$.

Let $\Pr$ be the probability measure of $\EE$.

Then the **probability** of $A$ is the value $\map \Pr A$.

## Also denoted as

Some sources denote the **probability** of an event $A$ as $\map P A$.

Some denote it $P \sqbrk A$.

## Popular Treatment

Amongst the non-mathematically-literate of the world's population, a common form of rhetorical emphasis (usually used when asserting a falsehood of a personal and delicate nature) is to state a greater-than-$100 \%$ probability of an event.

A typical example of this could be seen on the Maury Povich Show, as follows:

- Euniquea:
*I am five hundred thousand percent certain that Twyvone is the father of mah bay-bee ...* - Maury Povich:
*Twyvone ... you are*naaht*the father.*

## Sources

- 1963: Alexander M. Mood and Franklin A. Graybill:
*Introduction to the Theory of Statistics*(2nd ed.) ... (previous) ... (next): Chapter $1$: Introduction: $1.1$. Statistics - 1988: Dominic Welsh:
*Codes and Cryptography*... (previous) ... (next): Notation

- 1994: George E.P. Box, Gwilym M. Jenkins and Gregory C. Reinsel:
*Time Series Analysis: Forecasting and Control*(3rd ed.) ... (previous) ... (next):

- $1$: Introduction:
- $1.2$ Stochastic and Deterministic Dynamic Mathematical Models

- $1$: Introduction: