Welcome to Building Probability Models, the third course in your learning path! In the first two courses, you explored what probability means, learned how to identify sample spaces and outcomes, and discovered how experimental data can estimate the likelihood of events. That foundation puts you in a great position for what comes next: learning how to build, use, and evaluate probability models.

In this first lesson, we will look at what a probability model actually is and, more importantly, what makes one valid. By the end, you will be able to check any set of outcome–probability pairs and confidently say whether it qualifies as a proper probability model.

You might wonder why we insist on these two rules so strictly. The reason is practical: a probability model is meant to predict real outcomes. If a probability were negative, it would suggest something less likely than impossible, which has no real-world meaning. If probabilities summed to more or less than $1$, our model would claim that total chance is either too much or too little, leaving gaps or overlaps in our predictions.

When a model satisfies both requirements, we can trust it as a reliable starting point for making predictions. Later in this course, you will use valid models to forecast how often each outcome should appear over many trials and then compare those forecasts with observed data. Getting the foundation right here makes everything that follows more meaningful.