  A collection of $n$ random events is said to be $(n - 1)$-wise independent if
any $n - 1$ events among them are mutually independent. We characterise all
probability measures with respect to which $n$ random events are $(n - 1)$-wise
independent. We provide sharp upper and lower bounds on the probability that at
least $k$ out of $n$ events with given marginal probabilities occur over these
probability measures. The bounds are shown to be computable in polynomial time.
