In this chapter, we introduce the fourth, and since the 1990s, arguably one of the most important components of AI research. This is called the probabilistic, or often the stochastic, approach to understanding our world. It is used in applications across the AI spectrum including understanding, generating, and translating human languages; it is used for machine learning, vision systems, and the control of robots and other complex processes. We demonstrate the use of probabilistic models for diagnosing complex situations, including a program for the monitoring and control of nuclear power generation. The goal of this chapter is to offer computational accountability and epistemic sufficiency for the constructivist rapprochement and epistemic conjectures proposed in Chap. 7.