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 $\map \Pr A$.


Also denoted as

Some sources give the probability of $A$ as $\map P A$


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."


Sources