Independence in Probability - Law of Total Probability and Conditional Independence

Explore the fundamental concept of independence in probability theory through this 24-minute lecture that systematically builds from basic principles to advanced applications. Begin with the Law of Total Probability and learn how to calculate event probabilities by partitioning the sample space. Master the formal definition of independence for families of events, where intersection probabilities equal the product of individual probabilities, illustrated through practical examples including two coin tosses and countably infinite coin tosses. Discover conditional probability through its relative frequency foundation and understand why it constitutes a valid probability measure. Advance to conditional independence concepts, examining how events can be conditionally independent given another event, while analyzing counter-examples that clearly distinguish between standard independence and conditional independence.