Probability Solved Exercises

This volume has been conceived as a teaching aid for the study of probability, with particular attention to understanding the main theoretical concepts through a wide range of practical exercises. The proposed problems cover situations of varying difficulty and are designed to support both individual learning and classroom teaching. The aim is to strengthen the reader's ability to formulate, analyze and solve problems rigorously, making conscious use of mathematical notation and computational methods. The topics covered include set operations (union, intersection, difference) and their main properties, the concept of cardinality in relation to probability calculation, the principles of classical probability, the law of total probability, the law of conditional probability, Bayes' theorem and the analysis of mutually exclusive and independent events. Some exercises are inspired by real-world contexts, such as the analysis of health data, the effectiveness of diagnostic tests or scenarios related to business operations and production systems, in order to reinforce the connection between theory and practical application.