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