Abstract
Many processes in nature have uncertain outcomes. This means that their result cannot be predicted before the process occurs. A random process is a process that can be reproduced, to some extent, within some given boundary and initial conditions, but whose outcome is uncertain. Probability is a measurement of how favored one of the possible outcomes of such a random process is compared with any of the other possible outcomes.
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Note that in physics often event is intended as an elementary event. So, the use of the term event in statistics may sometimes lead to confusion.
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Or even different from 6, like in many role-playing games that use dices of non-cubic solid shapes.
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This apparent paradox is due to the French mathematician Joseph Louis François Bertrand (1822–1900).
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The coefficients present in the binomial distribution are the same that appear in the expansion of the binomial power (a + b)n. A simple iterative way to compute those coefficients is known in literature as the Pascal’s triangle. Different countries quote this triangle according to different authors, e.g.: the Tartaglia’s triangle in Italy, Yang Hui’s triangle in China, etc. In particular, the following publications of the triangle are present in literature:
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India: published in the tenth century, referring to the work of Pingala, dating back to fifth–second century bc.
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Persia: Al-Karaju (953–1029) and Omar Jayyám (1048–1131), often referred to as Kayyám triangle in modern Iran
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China: Yang Hui (1238–1298), referred to as Yang Hui’s triangle by Chinese; see Fig. 1.8
Fig. 1.8 
The Yang Hui triangle published in 1303 by Zhu Shijie (1260–1320)
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Germany: Petrus Apianus (1495–1552)
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Italy: Nicolò Fontana Tartaglia (1545), referred to as Tartaglia’s triangle in Italy
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France: Blaise Pascal (1655), refereed to as Pascal’s triangle.
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References
P. Laplace, Essai Philosophique Sur les Probabilités, 3rd edn. (Courcier Imprimeur, Paris, 1816)
A. Kolmogorov, Foundations of the Theory of Probability. (Chelsea Publishing, New York, 1956)
W. Eadie, D. Drijard, F. James, M. Roos, B. Saudolet, Statistical Methods in Experimental Physics. (North Holland, Amsterdam, 1971)
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Lista, L. (2016). Probability Theory. In: Statistical Methods for Data Analysis in Particle Physics. Lecture Notes in Physics, vol 909. Springer, Cham. https://doi.org/10.1007/978-3-319-20176-4_1
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