Borel-Cantelli Lemma

The Borel-Cantelli Lemma is a result in probability theory that helps determine whether certain events will happen many times or only a few times. It states that if the sum of the probabilities of a sequence of events is finite, then the chance that infinitely many of these events occur is zero—they happen only finitely often, almost never repeatedly. Conversely, if the events are independent and the sum of their probabilities diverges (becomes infinite), then these events will occur infinitely often, almost surely. Essentially, it links the likelihood of individual events to their long-term frequency.