Bayes' Theorem

Bayes' Theorem is a powerful tool that flips conditional probability on its head — it lets you update your belief about a cause after you have seen its effect. Instead of asking "given this cause, what is the chance of this outcome?", it answers the reverse: "given this outcome, what is the chance that this particular cause was responsible?" This idea of inverting probabilities is central to reasoning under uncertainty, from medical diagnosis to spam filtering. The theorem itself follows directly from the definition of conditional probability and the law of total pro …