Geodesic
Verification of data in certain problems of linear programming and the generalized Bernshtein problem
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 8 (2005) no. 3, pp. 231-244.

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We study the problem of finding the necessary and sufficient conditions of the fact that a given set of numbers could be a set of probabilities of certain events and probabilities of the pairwise interselection of such events. The algorithm of building a system of inequalities for solving this problem is obtained. The application of this algorithm to more general problems is discussed. 
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S. É. Lugovkin. Verification of data in certain problems of linear programming and the generalized Bernshtein problem. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 8 (2005) no. 3, pp. 231-244. http://geodesic.mathdoc.fr/item/SJVM_2005_8_3_a4/

[1] Nechepurenko M. I., “Intervalnye otsenki v bulevykh modelyakh nadezhnosti”, Tr. IVMiMG SO RAN. Ser. Sistem. modelirovanie, 4(22), Novosibirsk, 1997, 101–112

[2] Bernshtein S. N., Teoriya veroyatnostei, GTTI, M.-L., 1934

[3] Lugovkin S. E., Ob odnoi zadache Bernshteina (sluchai chetyrekh sobytii), Preprint / RAN. Sib. otd-nie. IVMiMG; 1158, Novosibirsk, 2003