Master combinatorial techniques, including permutations, combinations, and multinomial coefficients, to solve counting and probability problems.

Apply probability axioms, construct Venn diagrams, and calculate sample space sizes to evaluate probabilities in various scenarios.

Utilize Bayes' formula, the multiplication rule, and conditional probability to assess event relationships and solve real-world problems.

Analyze discrete and continuous random variables using probability density functions, cumulative distribution functions, and expected values.