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Sur la probabilité des évènements composés

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Référence : Sur la probabilité des évènements composés
Bulletin de la Société mathématique de France, 26, (1898), p.64-70


Résumé : Français

Sur la probabilité des événements composés

bulletin de la Société Mathématique de France 26 (1898) 64–70.

Delannoy rectifie un article du Révérent T.-C. Simmons de Grimsby de même titre qui critique la définition de de Moivre concernant les événements indépendants et le troisième principe de Laplace portant sur le calcul de la probabilité des événements indépendants. Delannoy montre que si sur les trois exemples de Simmons, la règle de Laplace y paraît en défaut, c’est que les événements ne sont pas indépendants.

(S. R. Schwer)

Résumé : Anglais

About the probability of composed events

Delannoy corrected an article of reverent T-C Simmons de Grimsby which has the same title as one which criticized de Moivre’s definition concerning independent events and Laplace’s third principle dealing with the computation of the probability of independent events. Delannoy shows that if in these three examples of Simmons, Laplace’s rule appears to be a failure, it is because the events are not independent.

(translated by Silvia Goodenough)


Nombre de citations :

AUTEBERT, Jean-Michel, LATAPY, Matthieu, et SCHWER, Sylviane R. (2002)
Le treillis des chemins de Delannoy.
Discrete Mathematics, vol. 258, no 1, p. 225-234.

SCHWER, Sylviane R. (2002) S-arrangements avec répétitions.
Comptes Rendus Mathematique, vol. 334, no 4, p. 261-266.

OPPENHEIM, A. C., BRAK, R., et OWCZAREK, A. L. (2002) Anisotropic step, surface contact, and area weighted directed walks on the triangular lattice.
International Journal of Modern Physics B, 2002, vol. 16, no 09, p. 1269-1299.

SULANKE, Robert A. (2003) Objects counted by the central Delannoy numbers.
J. Integer Seq, vol. 6, no 1.

EU, Sen-Peng (2003) On the quadratic algebraic generating functions and combinatorial structures. Thèse de doctorat. National Taiwan Normal University.

AUTEBERT, Jean-Michel, DECAILLOT Anne-Marie, et SCHWER Sylviane, (2003)
Henri-Auguste Delannoy et la publication des œuvres posthumes d’Edouard Lucas
. Gazette des mathématiciens : bulletin de liaison de la Société mathématique de France, n°95,p. 51-62.

BANDERIER, Cyril et SCHWER, Sylviane (2005) Why Delannoy numbers ?
Journal of statistical planning and inference, 2005, vol. 135, no 1, p. 40-54.

HETYEI, Gábor (2005) Central Delannoy numbers, Jacobi polynomials, and a new operation on balanced simplicial complexes," Combinatorics Seminar, University of South Carolina, March 22.

HETYEI, Gábor (2006) Central Delannoy numbers and balanced Cohen-Macaulay complexes. Annals of Combinatorics, vol. 10, no 4, p. 443-462.

HETYEI, Gábor.(2006) Central Delannoy numbers, Legendre polynomials, and a balanced join operation preserving the Cohen-Macaulay property. 18thinternational conference on "Formal Power Series and Algebraic Combinatorics", San Diego, CA, June 23.

SCHWER, Sylviane R. (2007) Temporal reasoning without transitive tables. arXiv preprint arXiv:0706.1290,

SCHRÖDER, Joachim (2007) Generalized Schröder numbers and the rotation principle. Journal of Integer Sequences, vol. 10, no 2, p. 3.

SCHRÖDER, Joachim (2007) Delannoy and tetrahedral numbers. Comment. Math. Univ. Carolin, vol. 48, no 3, p. 389-394.

HETYEI, Gábor (2008) Delannoy numbers and Legendre polytopes. Proceedings of the20th international conference on "Formal Power Series and Algebraic Combinatorics", Valparaiso, Chile, June 23-27.

HETYEI, Gábor (2008) Delannoy numbers and a combinatorial proof of the orthogonality of the Jacobi polynomials with natural number parameters. 23rd Clemson mini-Conference on Discrete Mathematics and Algorithms, Clemson, SC, October 2.

HETYEI, Gábor (2008) Delannoy numbers and the orthogonality of certain Jacobi polynomials," Algebra and Combinatorics Seminar, Mathematics Department, NC State University, September 12.

HETYEI, Gábor (2008) Links We Almost Missed Between Delannoy Numbers and Legendre Polynomials. Billerafest 2008, June 13-15.

KISELMAN, Christer (2008) Functions on discrete sets holomorphic in the sense of Ferrand, or monodiffric functions of the second kind. Science in China Series A : Mathematics, vol. 51, no 4, p. 604-619.

HETYEI, Gábor (2009) Delannoy orthants of Legendre polytopes.
Discrete & Computational Geometry, vol. 42, no 4, p. 705-721.

HETYEI, Gábor (2009) Shifted Jacobi polynomials and Delannoy numbers. arXiv preprint arXiv:0909.5512,

HETYEI, Gábor (2009) Geometric interpretations of the relation between Delannoy numbers and Legendre polynomials," colloquium talk at the Department of Mathematical Sciences, George Mason University, November 20.

杨 金花 et 田冲 (2009) Delannoy 数的计算公式与卷积和. 周口师范学院学报, 2009, vol. 26, no 2, p. 11-13.

田冲 et 杨金花 (2009). Delannoy 数的卷积和. 平顶山学院学报, vol. 24, no 2, p. 66-68.

DZIEMIANCZUK, M. (2013) Generalizing Delannoy numbers via counting weighted lattice paths. INTEGERS, vol. 13, 34 p.

VELASCO, Claudio de Jesús Pita Ruiz (2010). Convolution and Sulanke numbers. Journal of Integer Sequences, vol. 13, no 2, p. 3.

SAMIEINIA, Shiva (2010) The number of continuous curves in digital geometry. Portugaliae Mathematica, vol. 67, no 4, p. 75.

MEIJER, Johannes W. (2010) Famous numbers on a Chessboard. Acta Nova, vol. 4, p. 589.

DZIEMIANCZUK, Maciej (2014) On Directed Lattice Paths With Additional Vertical Steps. arXiv preprint arXiv:1410.5747.

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