Why do so many students find probability difficult? Could it be the way the subject is taught in so many textbooks? When I was a student, a class in topology made a great impression on me. The teacher asked us not to take notes during the first hour of his lectures. In that hour, he explained ideas and concepts from topology in a non-rigorous, intuitive way. All we had to do was listen in order to grasp the concepts being introduced. In the second hour of the lecture, the material from the first hour was treated in a mathematically rigorous way and the students were allowed to take notes. I learned a lot from this approach of interweaving intuition and formal mathematics.

This book is written very much in the same spirit. It first helps you develop a “feel for probabilities” before presenting the more formal mathematics. The book is not written in a theorem–proof style. Instead, it aims to teach the novice the concepts of probability through the use of motivating and insightful examples. No mathematics are introduced without specific examples and applications to motivate the theory. Instruction is driven by the need to answer questions about probability problems that are drawn from real-world contexts. The book is organized into two parts. Part One is informal, using many thought-provoking examples and problems from the real world to help the reader understand what probability really means. Probability can be fun and engaging, but this beautiful branch of mathematics is also indispensable to modern science.