Definition:Probability
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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 $\mathcal E$ be an experiment.
Let $A \in \Sigma$ be an event in the event space $\Sigma$ of $\mathcal E$.
Let $\Pr$ be the probability measure of $\mathcal E$.
Then the probability of $A$ is the value $\Pr \left({A}\right)$.
Comment
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."
