As I work through the refresher on probability and information theory, the authors showcase Bayes’ Rule which is a key statistical technique applied to e-mail filtering.

We often find ourselves in a situation where we know $P\left(y|x\right)$ and need to know $P\left(x|y\right)$. Fortunately, if we also know $P\left(x\right)$, we can compute the desired quantity using Bayes’ rule: