I have a large (N) list of results from a process that is either positive or negative. After examining X of them and receiving only positive results, how certain can I be that the list only contains positive results (with probability P)?
Context: I'm processing the results (between several thousand and several billion) of a process and am given a list of values that take a few seconds each to evaluate as passing/failing. I only need to be reasonably certain that everything passed to pass the batch for most jobs. For some jobs, 100% certainty is necessary, and they'll all need to be checked. For the others, how many do I need to check to be P% certain that there are no fails?