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What is a probability?

What is a probability? Here are some definitions.

Noun
  1. the state of being probable; likelihood
  2. an event that is likely to occur
  3. the relative likelihood of an event happening
  4. (mathematics) a number, between 0 and 1, expressing the precise likelihood of an event happening
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Examples
A gambler usually wagers more after taking a loss, in the misguided belief that a run of bad luck increases the probability of a win.
A single world language would in all probability do very little to advance peace.
These maps graphically illustrate the change in earthquake probability during aftershock and possible foreshock sequences.
Life expectancy is a term used by actuaries, people who calculate statistics and probability for insurance use.
Yet aggregating the collective wisdom and putting a probability on it is a very valuable function in itself.
Some countries recognise abortion when pregnancy results from rape or incest, or when there is a high probability of foetal impairment.

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