Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Probability through Algebra is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. But this book isn't a ``course' in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes, and one of the goals of the problem sets is for readers to uncover these themes for themselves. The specific themes developed in Probability through Algebra introduce readers to the algebraic properties of expected value and variance through analysis of games, to the use of generating functions and formal algebra as combinatorial tools, and to some applications of these ideas to questions in probabilistic number theory. Probability through Algebra is a volume of the book series IAS/PCMI-The Teacher Program Series published by the American Mathematical Society. Each volume in that series covers the content of one Summer School Teacher Program year and is independent of the rest.