Lesson 1

Bayes' formula is a formula in probability theory that relates the conditional probabilities of two events and has applications in fields such as medical diagnosis, spam filtering, machine learning, finance, genetics, weather forecasting, and others. The formula itself is unexpectedly simple and directly follows from the definition of conditional probability: \[\Pr[A \mid B] = \frac{\Pr[B \mid A]}{\Pr[B]}\cdot \Pr[A] \ .\] Informally speaking, it shows how to adjust our estimate of the probability of event \(A\) occurring if we know that event \(B\) has occurred: we need to multiply \(\Pr[A]\) by \(\frac{\Pr[B \mid A]}{\Pr[B]}\).