 
Summary: A Lower Bound on the Probability of a Finite Union
of Events with Applications \Lambda
Hongyan Kuai, Fady Alajaji and Glen Takahara
Mathematics and Engineering
Department of Mathematics and Statistics
Queen's University
Kingston, Ontario, Canada K7L 3N6
Abstract
A new lower bound on the probability of
P(A 1 [ \Delta \Delta \Delta [ AN ) is established in terms of only
the individual event probabilities P(A i )'s and
the pairwise event probabilities P(A i `` A j )'s.
This bound is shown to be always at least
as good as two similar lower bounds, one by
de Caen (1997) and the other by Dawson and
Sankoff (1967). Numerical examples for the
computation of this inequality are also pro
vided. Finally, the application of this re
sult to the symbol error probability of an un
coded communication system used in conjunc
