Probability
Counting Trees – Branching Diagrams for Counting
A counting tree uses the same branching structure as the tree diagrams you've already used in probability, but now purely to count outcomes rather than calculate probabilities. Each level of the tree represents one stage of choice, and every complete path from the trunk to a final branch tip represents one unique outcome.
Unlike a counting table, a tree handles any number of stages, not just two – simply add another level of branching for each additional choice. The total number of final branch tips is the total number of possible outcomes.
Counting with a Tree
Each level of branching represents one choice. The total number of final branch tips equals the total number of outcomes.
Each of the 3 starter branches splits into 2 main branches: 3 × 2 = 6 final branches.
Real-Life Application
- Decision-making: a decision tree maps out every possible sequence of choices and their outcomes.
- Game strategy: game trees map out every possible sequence of moves in a game.
- Troubleshooting guides: a diagnostic flowchart is structured exactly like a counting tree.
Key Takeaways
- A counting tree branches once for each stage of choice.
- Every complete path represents one unique outcome.
- Trees handle any number of stages, unlike a two-dimensional table.