The Law of Rare Events

The Law of Rare Events states that the probability of a specific rare event occurring in a fixed interval is directly proportional to the length of that interval, assuming events happen independently at a constant average rate. In simpler terms, the chance of an uncommon event happening increases gradually with more time or opportunities, but remains low overall. For example, the likelihood of a rare disease appearing in a person is tiny each day, but over many years, the probability accumulates. This law helps in predicting outcomes for infrequent occurrences in fields like insurance, statistics, and risk management.