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We give exponential upper bounds for $P(S \le k)$, in particular $P(S=0)$,where $S$ is a sum of indicator random variables that are positivelyassociated. These bounds allow, in particular, a comparison with theindependent case. We give examples in which we compare with a famousexponential inequality for sums of correlated indicators, the Jansoninequality. Here our bound sometimes proves to be superior to Janson's bound.

Large deviation upper bounds for sums of positively associated indicators