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Discrete probability problems

These problems will have to do with:

Part 1: Counting
Sets and their Counting
Sum Rule
Partition Method
Difference Method
Bijection Method
Product Rule
Generalized product rule
Pigeonhole Principle
Inclusion/Exclusion
Combinatorial nature of binomial coefficients

Part 2: Probability
Sample space
Axioms of probability
Conditional probability
Independence
Bayes rule
Random Variables
Expectation and Linearity
Variance

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