What Is a Tree Diagram?

What Is a Tree Diagram?

A tree diagram shows all the possible outcomes of an event and their probabilities.

A Real Example of a Tree Diagram

It is easier to understand a tree diagram with an example.

Tossing a Coin

If a coin is tossed, the coin can land on Heads or Tails.

  • Each outcome has its own branch. There is a branch for Heads and for Tails.

  • The probability of each outcome is written by each branch. The probability of Heads (12) is written by the branch. The probability of Tails (12) is written by the branch.

Note: The probabilities across the branches add up to 1. They are mutually exclusive and exhaustive events.

Another Real Example of a Tree Diagram

A tree diagram can be extended to more than one event.

The tree diagram below is for two coin tosses.

See Also

What is probability? What are mutually exclusive events?