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Explore fundamental concepts of probability theory in this lecture from MIT's Principles of Discrete Applied Mathematics course. Learn what it means for two events to be independent and understand the concept of conditioning one event on another. Master the law of Total Probability and Bayes' rule, essential tools for calculating probabilities in complex scenarios. Discover the definition and properties of random variables and expectations, culminating in an explanation of the linearity of expectation principle. This 71-minute lecture provides rigorous mathematical foundations while building intuition for these core probabilistic concepts that form the basis for more advanced topics in discrete mathematics and probability theory.
