Bounds on the
probability of the union of the events
The problem of finding lower and upper bounds for the probability of the union of finite number of events has a vast literature. A bound of this type is typically based on some probabilities of the intersections of events not more than a previously given number, the order of the bounds. These bounds provide us a powerful tool in a number of applications such as calculating the values of multivariate distribution functions, estimating network reliability and solving stochastic programming problems. Some of these bounds will be reviewed and discussed.