# Tree Diagram

Sub Topics
The study of probability includes many definitions, formulas and calculations. The tree diagram is a simple approach which gives a visual expression for the experiment conducted and the expected results. The presentation of the problem as a tree brings in clarity to the concept of probability as a whole.

## Tree Diagram Definition

A tree diagram is a tool which connects the outcomes of an experiment from the starting point through branches like straight lines.
In compound events each possible outcome lead to further resulting points, the complete picture consisting of branching lines resemble a tree. It is used to determine all possible outcomes of a probability experiment.
The tree diagram can be used to visualize the sample space for both the independent and dependent events, and the events that follow a sequential order.

## How to Make a Tree Diagram

Suppose an experiment has a sequence of three trials repeated or different. The starting point and the three trials are aligned in a horizontal order. The points representing the outcomes are aligned vertically under each trial. The starting point and the outcomes of the first trial are joined with a line. The outcomes of first trial are then connected with the corresponding outcomes of the second trail and these are in turn connected with the outcomes of the further trial.

The end points represent final outcomes in the sample space.

## Tree Diagram Probability

The tree diagrams are not only helpful in listing the sample space but they also help the students to solve compound probability problems when the events occur in sequence.

## Tree Diagram Math Problems

Can a template for tree diagram be used?

The tree diagrams for some problems will resemble. For example the tree diagram drawn to record the outcomes of three tosses of a coin will resemble the tree diagram showing the possible sex combinations of three children in a family. Because each trial in these two experiments have same number of outcomes (two), hence the probability of a simple event is same in both cases.

Hence the tree diagram given for Family of three children can be used for three tosses of a coin changing the labels suitably. In order that a given or known tree diagram may be used for another problem, it is necessary that both the problems have the same number of sequence or trials, and number of outcomes in each sequence is same.