Probability theory provides the foundation for understanding uncertainty in fields ranging from finance and insurance to engineering and data science. This textbook is designed for undergraduate actuarial students seeking a clear, practical, and mathematically sound introduction to the subject. Requiring only a first course in calculus, it develops core ideas in a structured and accessible way, making it suitable for a one-semester course as well as for independent study.

What sets this book apart is its balanced approach between intuition and rigor. Rather than relying heavily on measure-theoretic formalism or focusing solely on computational techniques, it introduces essential concepts-such as probability spaces-in a gradual and approachable manner. By combining theoretical development with computational tools, the text bridges the gap between abstract understanding and real-world application, preparing students for both academic study and professional practice.

Key features:

• A balanced presentation that introduces foundational concepts of probability without heavy measure-theoretic machinery
• Clear, step-by-step development starting from set theory and building toward probability models and applications
• Numerous practice questions adapted from Society of Actuaries Probability (P) exam materials
• Selected solutions with detailed explanations to support self-study and deeper understanding
• Integrated Python simulations in every section to illustrate concepts and verify results
• Accompanying Jupyter notebooks available online for interactive learning and experimentation

By combining mathematical rigor, practical exercises, and modern computational tools, this book offers a solid introduction to probability theory. It is ideal for actuarial students preparing for professional exams, while also serving as a valuable resource for students in related fields who seek a solid and engaging foundation in probability.

Guojun Gan is an Associate Professor in the Department of Mathematics at the University of Connecticut, where he has served since August 2014, following six years in a major life insurance company in Toronto and one year at a hedge fund in Oakville, Canada. He holds a B.S. from Jilin University (2001) and M.S. and Ph.D. degrees from York University (2003 and 2007), and is a Fellow of the Society of Actuaries (FSA). His research spans actuarial science and data science, and he has authored several books and numerous peer-reviewed publications on topics such as data clustering, variable annuities, loss models, applied statistics, programming, and mathematical finance.