In preparation for studying rendering techniques, we now discuss Monte Carlo integration. We start with a rapid review of ideas from discrete probability theory, and then generalize to continua like the real line or the unit sphere. We apply these notions to describe how to generate random samples from various sets. We then introduce Monte Carlo integration, treating all the basic ideas through the integration of a function on an interval [a, b], where the ideas are easiest to understand. We then show how these ideas apply to integration on a hemisphere or sphere, and hence how they are used to find reflected radiance via the reflectance equation, for instance.