Historically, the original purpose of the theory of probability was to describe the exceedingly narrow domain of experience connected with games of chance, and the main effort was directed to the calculation of certain probabilities.

Probability is the mathematics of uncertainty. ...many modern theories have uncertainty built into their foundations. Thus learning to think in terms of probability is essential.

Translation: "One sees, from this Essay, that the theory of probabilities is basically just common sense reduced to calculus; it makes one appreciate with exactness that which accurate minds feel with a sort of instinct, often without being able to account for it."

Probability is not a mere computation of odds on the dice or more complicated variants; it is the acceptance of the lack of certainty in our knowledge and the development of methods for dealing with our ignorance.

Many modern philosophers claim that probability is relation between an hypothesis and the evidence for it.

Probability is expectation founded upon partial knowledge. A perfect acquaintance with all the circumstances affecting the occurrence of an event would change expectation into certainty, and leave neither room nor demand for a theory of probabilities.

The theory of chance consists in reducing all the events of the same kind to a certain number of cases equally possible, that is to say, to such as we may be equally undecided about in regard to their existence, and in determining the number of cases favorable to the event whose probability is sought.

The classical theory of probability was devoted mainly to a study of the gamble's gain, which is again a random variable; in fact, every random variable can be interpreted as the gain of a real or imaginary gambler in a suitable game.

Probability is not about the odds, but about the belief in the existence of an alternative outcome, cause, or motive.

The theory of randomness is fundamentally a codification of common sense.

Probability is the intersection of the most rigorous mathematics and the messiest of life.

Probability was only invented a few hundred years ago. It's not a natural way to think at all. It's extremely difficult and complex. Anything that can help people do it, is of benefit.

It has seemed to me that the theory (calcul) of probabilities ought to serve as the basis for the study of all the sciences, and particularly of the sciences of observation.

In general statistics can be considered as the offspring of the theory of probability, it builds on its parent and extends the area of patronymic jurisdiction.