Probability and Independence

This lecture covers the concepts of probability and independence in the context of events occurring in a probability space. Starting with basic examples of families with two children, it delves into the definition of independence and various types of independence between events. The law of total probabilities is introduced to calculate probabilities in different scenarios. The lecture also explores parallel and serial systems in reliability theory, discussing how the probability of system failure changes based on the components' operations. The importance of independence in simplifying probability calculations is emphasized, along with practical implications in decision-making processes.