The author presents a textbook based on his elementary probability courses for students of specializations outside mathematics. It is well suited for classroom use as well as for self-study. The key areas described in the book are the basic concepts of probability (including sample spaces and random events), conditional probability and independence, random variables, their distributions and expectation values, sampling with and without replacement and some simple statistical tests. Only discrete random variables and models are introduced. Explanation is based on examples rather than a theory so that the only prerequisite is knowledge of basic high school algebra. Examples are mainly oriented to practical situations (such as different problems in economy, sports, elections, drug testing, cryptology, etc.). Each chapter contains a variety of exercises and problems to solve. The chosen approach is practical and entertaining. The book is a useful tool for teachers and for anybody interested in the basic ideas and applications of classical probability theory.