MIT professor Ankur Moitra continues his course 18.200, Principles of Discrete Applied Mathematics, with a lecture on the foundations of probability. He defines what it means for two events to be independent, then introduces conditioning, working through the law of Total Probability and Bayes' rule with worked examples on the board. The second half of the lecture turns to random variables, covering expectation and proving linearity of expectation, the property that lets you compute the expected value of a sum by adding individual expectations even when the variables are dependent. The seventy-one minute session is blackboard-style, Moitra building each definition from the last and pausing to work through small examples before stating the general theorems, aimed at students who already have the basic axioms of probability and are moving toward applications in discrete mathematics and combinatorics.