Counting determines how many possible outcomes arise in probability and combinatorics. It provides a foundation for quantifying uncertainty, assessing risk, and structuring later statistical problem solving. section 2.0 section 2.2
Use two fundamental rules to count outcomes:
- Apply the multiplication rule when events occur simultaneously or sequentially; multiply the numbers of choices across stages. section 2.2
- Apply the addition rule when scenarios are mutually exclusive; add their possible outcomes. section 2.2
- Distinguish counting rules from combinations and permutations, which address different arrangements and selections of objects. section 2.0 section 1.4.3
Counting belongs among the basic probability concepts that precede random variables, probability distributions, and more advanced quantitative techniques. Its role is conceptual and computational: clarify the outcome structure before calculating probabilities or interpreting uncertainty. section 2.0 section 1.4.3
