# Definition:Probability/Formal Definition

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## Probability

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 give the **probability** of $A$ as $\map P A$

## 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

- 1965: A.M. Arthurs:
*Probability Theory*... (previous) ... (next): Chapter $2$: Probability and Discrete Sample Spaces: $2.3$ Probabilities in discrete sample spaces - 1986: Geoffrey Grimmett and Dominic Welsh:
*Probability: An Introduction*... (previous) ... (next): $1$: Events and probabilities: $1.3$: Probabilities - 2013: Donald L. Cohn:
*Measure Theory*(2nd ed.) ... (previous) ... (next): $10$: Probability: $10.1$: Basics