If we have the inclusion exclusion principle of the following generalized form,
$$P\left(\bigcup_{i=1}^n A_i\right) = \sum_{k=1}^n (-1)^{k-1} \sum_{I\subset \{1,\ldots,n \} ; \|I\| = k } P(A_I)$$
and we take a limit of $n \to \infty$, does that approach $1$?
Usecase: We have a bug in a software which is extremely unlikely to occur -- but if it is going to be used in an extremely large userbase, it's likely that it will surface somewhere. I want to get a general probability about this occurrence.