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Probabilistic Models

In this video, we introduce probabilistic models — the mathematical framework used to describe uncertainty. You’ll learn the two key ingredients of any probabilistic model: the sample space (the set of all possible outcomes) and the probability law (which assigns probabilities to events). We explain the three fundamental probability axioms — nonnegativity, additivity, and normalization — and see how they shape our understanding of probability. Through examples with coins, dice, darts, and even Romeo and Juliet, we explore the difference between discrete and continuous models, and why single points in a continuous sample space have probability zero. By the end, you’ll be able to: Define sample spaces and events Understand what makes a valid probability law Calculate probabilities in discrete and continuous settings