Introduction to Probability and Risk Analysis

We talk about risk and likelihood every day, but translating these intuitive concepts into precise mathematical terms is key to unlocking advanced data analysis, decision-making, and statistical modeling. This text-only course bridges the gap between everyday intuition and rigorous mathematical reality. You will start with the fundamental terminology of events and sample spaces, progress to calculating complex probabilities, and learn how modern data analysts use these concepts to model uncertainty. What you'll learn: - Understand the core terminology of probability, including experiments, sample spaces, and events - Calculate the likelihood of simple, compound, and mutually exclusive events using standard mathematical formulas - Apply conditional probability and Bayes' theorem to update predictions based on new information - Analyze real-world risk and decision-making scenarios using expected value and probability distributions - Practice modeling uncertainty with modern data-science concepts like random variables and basic statistical simulations This course begins with foundational definitions and basic rules of probability before guiding you through structured written exercises and practical calculation scenarios. It is designed for beginners who want to build a strong quantitative foundation without any prior mathematical prerequisites. Dive into the text and start thinking like a statistician today.