The tutorial first reviews the fundamentals of probability (but to do that properly, please see the earlier Andrew lectures on Probability for Data Mining). It then discusses the use of Joint Distributions for representing and reasoning about uncertain knowledge. Having discussed the obvious drawback (the curse of dimensionality) for Joint Distributions as a general tool, we visit the world of clever tricks involving indepedence and conditional independence that allow us to express our uncertain knowledge much more succinctly. And then we beam with pleasure as we realize we've got most of the knowledge we need to understand and appreciate Bayesian Networks already. The remainder of the tutorial introduces the important question of how to do inference with Bayesian Networks (see also the next Andrew Lecture for that).