So far you have described data that already exists. Probability flips the question around: given what you know, how likely is something that hasn’t happened yet? It is the mathematics of uncertainty, and it is the bridge between the descriptive statistics you have learned and the inference you will reach at the end of this course. Every confidence interval, every p-value, every machine-learning model that outputs a “70% chance” rests on the ideas in this module.

You will start by learning the two ways to pin a number on chance — estimating from data (relative frequency) and calculating from theory (equally likely outcomes) — and watch them converge as samples grow. Then you will learn the rules that let you combine events: the addition rule for “or,” the multiplication rule for “and,” complements for “at least one,” and the crucial idea of independence. You will finish with permutations and combinations, the counting tools that make otherwise impossible probability questions tractable.

You will work in Python throughout — simulating coin flips and dice with numpy, estimating real probabilities from the penguins dataset, and finally computing the genuinely tiny odds of winning a lottery. By the end you will reason about chance precisely instead of by gut feeling.

Start with Lesson 1, where you will learn the two faces of probability and the law that ties them together.