Physical probabilities or chances exist and come in many types. Some feature in fundamental physics, others feature in the special sciences. What unites them, on my view, is their epistemological role. Part I of my dissertation lays out this role. It expands David Lewis's principal principle to incorporate chances from special sciences like biology as well as fundamental physics, and discusses how we know these chances and why that knowledge is so valuable. Part II is concerned specifically with the chances in quantum mechanics and a problem that neither philosophers nor physicists have yet to appreciate. This problem, which I call the control problem, contrasts from the well-known measurement problem, and places new fundamental constraints on our quantum theories. Part III explores the limits of our mathematical models of chance. It focuses on the role of probabilistic independence in chance judgments, discussing puzzles with certain of those judgments, as well as with the traditional mathematical definition of probabilistic independence.