On the probability of union in the n-space

In this paper, our sets are orthants in Rn and N, the number of them, is large (N>n). We introduce the modified inclusion-exclusion formula in order to efficiently calculate the probability of a union of such events. The new formula works in the bivariate case, and can also be used in Rn,n≥3 with a condition on the projected sets onto lower dimensional spaces. Numerical examples are presented.