Harder topics in an calc based intro to probability class?

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Make sure you have a good intuitive understanding of the operations on sets (union, intersection, exclusion, DeMorgan's law, etc). If that is done, the best thing you can do is start reading the text you're going to use and do problems in combinatoric. Combinatorics is very important for the rest of the class. The easiest part in my opinion comes at the end, with "Continuous random variables".