Commun. Korean Math. Soc. 2003 Vol. 18, No. 4, 725-736 Printed December 1, 2003

Min-Young Lee, Moon-Shik Jo Dankook University, Dankook University

Abstract : Let $ A_1, A_2, \cdots , A_n $ be a sequence of events on a given probability space. Let $m_n$ be the number of those $A_j's$ which occur. Upper bounds of $P(m_n \geq 1)$ are obtained by means of probability of consecutive terms which reduce the number of terms in binomial moments $S_{2,n}, S_{3,n}$ and $S_{4,n}$.

Keywords : binomial moment, Bonferroni-type inequality, method of indicators