# History of probability

Probability |
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Probability deals with random experiments with a known distribution, Statistics deals with inference from the data about the unknown distribution.

## Etymology

*Probable* and *probability* and their cognates in other modern languages derive from medieval learned Latin *probabilis*, deriving from Cicero and generally applied to an opinion to mean *plausible* or *generally approved*.^{[1]} The form *probability* is from Old French *probabilite* (14 c.) and directly from Latin *probabilitatem* (nominative *probabilitas*) "credibility, probability," from *probabilis* (see probable).
The mathematical sense of the term is from 1718. In the 18th century, the term *chance* was also used in the mathematical sense of "probability" (and probability theory was called *Doctrine of Chances*). This word is ultimately from Latin *cadentia*, i.e. "a fall, case". The English adjective *likely* is of Germanic origin, most likely from Old Norse *likligr* (Old English had *geliclic* with the same sense), originally meaning "having the appearance of being strong or able" "having the similar appearance or qualities", with a meaning of "probably" recorded mid-15 c. The derived noun *likelihood* had a meaning of "similarity, resemblance" but took on a meaning of "probability" from the mid 15th century. The meaning "something likely to be true" is from 1570s.

## Origins

Ancient and medieval

^{[2]}

In Renaissance times, betting was discussed in terms of odds such as "ten to one" and maritime insurance premiums were estimated based on intuitive risks, but there was no theory on how to calculate such odds or premiums.^{[3]}

The mathematical methods of probability arose in the investigations first of Gerolamo Cardano in the 1560s (not published until 100 years later), and then in the correspondence Pierre de Fermat and Blaise Pascal (1654) on such questions as the fair division of the stake in an interrupted game of chance. Christiaan Huygens (1657) gave a comprehensive treatment of the subject.^{[4]}^{[5]}

In ancient times there were games played using astragali, or talus bone.^{[6]} The pottery of ancient Greece provides evidence to show that the astragali were tossed into a circle drawn on the floor, much like playing marbles. In Egypt, excavators of tombs found a game they called "Hounds and Jackals", which closely resembles the modern game snakes and ladders. According to Pausanias,^{[7]} Palamedes invented dice during the Trojan wars, although their true origin is uncertain. The first dice game mentioned in literature of the Christian era was called hazard. Played with two or three dice, it was probably brought to Europe by the knights returning from the Crusades. Dante Alighieri (1265–1321) mentions this game. A commenter of Dante puts further thought into this game: the thought was that with three dice, the lowest number you can get is three, an ace for every die. Achieving a four can be done with three dice by having a two on one die and aces on the other two dice.^{[8]}

Cardano also thought about the sum of three dice. At face value there are the same number of combinations that sum to 9 as those that sum to 10. For a 9:(621) (531) (522) (441) (432) (333) and for 10: (631) (622) (541) (532) (442) (433). However, there are more ways of obtaining some of these combinations than others. For example, if we consider the order of results there are six ways to obtain (621): (1,2,6), (1,6,2), (2,1,6), (2,6,1), (6,1,2), (6,2,1), but there is only one way to obtain (333), where the first, second and third dice all roll 3. There are a total of 27 permutations that sum to 10 but only 25 that sum to 9. From this, Cardano found that the probability of throwing a 9 is less than that of throwing a 10. He also demonstrated the efficacy of defining odds as the ratio of favourable to unfavourable outcomes (which implies that the probability of an event is given by the ratio of favourable outcomes to the total number of possible outcomes).^{[9]}^{[10]}

In addition,

^{[11]}

## Eighteenth century

*The Doctrine of Chances*(1718) put probability on a sound mathematical footing, showing how to calculate a wide range of complex probabilities. Bernoulli proved a version of the fundamental law of large numbers

## Nineteenth century

The power of probabilistic methods in dealing with uncertainty was shown by

*Théorie analytique des probabilités*in which he consolidated and laid down many fundamental results in probability and statistics such as the moment-generating function, method of least squares, inductive probability

Towards the end of the nineteenth century, a major success of explanation in terms of probabilities was the

The field of the history of probability itself was established by Isaac Todhunter's monumental *A History of the Mathematical Theory of Probability from the Time of Pascal to that of Laplace* (1865).

## Twentieth century

Probability and statistics became closely connected through the work on

^{[12]}

The theory of stochastic processes broadened into such areas as

The twentieth century also saw long-running disputes on the

The mathematical treatment of probabilities, especially when there are infinitely many possible outcomes, was facilitated by Kolmogorov's axioms (1933).

## References

**^**Franklin (2001), pp. 113, 126.**^**Franklin (2001).**^**Franklin (2001), pp. 278–288.**^**Hacking (2006). For Cardano, see p. 54; for Fermat and Pascal, see pp. 59–61; for Huygens, see pp. 92–94**^**Franklin (2001), pp. 296–316.- ISBN 978-0-85264-171-2.
**.****^**Franklin (2001), pp. 293–294.**^***Some laws and problems in classical probability and how Cardano anticipated them*Gorrochum, P.*Chance*magazine 2012**^**Franklin (2001), pp. 296–300.**^**Franklin (2001), p. 302.**^**Salsburg (2001).**^**Bernstein (1996), Chapter 18.

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**## Sources

- ISBN 0-471-12104-5.
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- McGrayne, Sharon Bertsch (2011).
*The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy*. New Haven: Yale University Press.ISBN 9780300169690. - von Plato, Jan (1994).
*Creating Modern Probability: Its Mathematics, Physics and Philosophy in Historical Perspective*. New York: Cambridge University Press. . - Salsburg, David (2001).
*The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century*. Henry Holt and Company. . - .

## External links

- JEHPS: Recent publications in the history of probability and statistics
- Electronic Journ@l for History of Probability and Statistics/Journ@l Electronique d'Histoire des Probabilitéet de la Statistique
- Figures from the History of Probability and Statistics (Univ. of Southampton)
- Probability and Statistics on the Earliest Uses Pages (Univ. of Southampton)
- Earliest Uses of Symbols in Probability and Statistics on Earliest Uses of Various Mathematical Symbols