On extreme joint probabilities of k events chosen from n events | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2018. № 39. DOI: 10.17223/20710410/39/1

An arbitrary probability space with n events is considered. All events have the same probability p. No restrictions on correlations between the events are imposed and the events are considered simply as arbitrary subsets of measure p in the probability space. From the set of n events, all C/k subsets X consisting of k events are chosen, and for each such subset X the probability P(X) of joint implementation of its k events is considered. The subset with the minimum probability min P(X) and X:|X|=fc the subset with the maximum probability max P(X) are selected. In the paper, X :|X |=fc exact boundaries for both probabilities are obtained. For minimum probability: if kp @ k - 1, then 0 @ min P(X) @ p; X:|X|=fc if kp > k - 1, then kp - k + 1 @ min P(X) @ p. X:|X|=fc For maximum probability: if np < k - 1, then 0 ^ max P(X) ^ p; X:|X|=fc if k if k ^ np, then , , np - IПРI 1 ^ np < k, then -^ max P(X) ^ p; СП X:|X|=fc ^{v 7} ^ max P(X) ^ p. X :|X |=fc ⁽M +^{1 - n}p^)C f_rapJ + ⁽ⁿp ^- LⁿpJ^)Cf_rapJ+i C k ^Cn