Tree Diagrams

A tree diagram looks like a tree with branches. Each branch shows a choice or outcome. Tree diagrams help you see every possibility and count them up. They are very useful in probability.

How to Draw One

Start with a dot on the left. Draw branches for each choice. If you flip a coin, draw two branches: one for heads and one for tails.

If you flip the coin again, draw two more branches from each of the first branches. Now you can see all four possible outcomes: heads-heads, heads-tails, tails-heads, and tails-tails.

Counting Outcomes

Tree diagrams make it easy to count all possible results. If you have 3 shirts and 2 pairs of pants, a tree diagram shows you have 6 different outfits. That is 3 times 2.

This works for bigger problems too. If you pick an appetizer, a main dish, and a dessert from a menu, a tree diagram shows all the meal combinations.

Fun Facts

• A tree diagram for flipping a coin 3 times has 8 endpoints, showing 8 possible outcomes.
• Tree diagrams are used by sports teams to plan strategies for games.
• Scientists use tree diagrams to study how traits are passed from parents to children.

Did You Know?

If you flip a coin 10 times, a tree diagram would have 1,024 endpoints! The number of possibilities doubles with each flip.