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 $\map P A$ or $\map {\mathrm P} A$.
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.
Also see
- Results about probability can be found here.
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:
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): probability
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): probability