Most real questions about probability come with a condition attached. Not “what is the chance of rain?” but “what is the chance of rain given that the sky is grey?” Not “is this email spam?” but “is this email spam given the words it contains?” This module is about that little word — given — and the surprisingly powerful machinery built on top of it.

You will start with conditional probability: how knowing that one event happened changes the probability of another. From there you will build to Bayes’ theorem, one of the most important equations in all of data science — the rule for updating a belief when new evidence arrives. Along the way you will meet a famous, counterintuitive result: why a positive result on a 99%-accurate medical test can still mean you are probably healthy.

Then you will put it to work. The Naive Bayes algorithm turns Bayes’ theorem into a real, working classifier, and you will build one from scratch — no machine-learning library — to tell genuine news headlines from clickbait, on a dataset of 6,000 real headlines. By the end you will understand not just the formula, but the idea that lets a machine weigh evidence and change its mind.

Start with Lesson 1 and the question that anchors the whole module: what does it mean to know something given something else?