Tree diagrams find their use in probability theory. They can easily show the events are formed from more than one independent event. Tree diagrams are also used in decision trees, event trees. In a tree diagram, first the branching is done based on the first statement and then to the each of those branches, again branching is done based on the second statement. 

Word Problems

Problem 1:

In a game, there are three doors A, B, C and 3 windows after each door to get to the next point. How many choices will be there for a person to get to the next point?


The tree diagram will give the branching of doors first, and then for each door there will be branching of windows.

Tree Diagram Example
Problem 2:

There are 4 Kings from a deck of card. One coin is tossed and one card is chosen from those 4 Kings. Find the sample space.


The tree diagram for the sample space is given below.

Sample Space Using Tree Diagram
Problem 3:

An email comes in your email box which you will reply based on if it is urgent or not. Make a decision tree for this.


Given is the decision tree showing process of taking the right step.

Tree Diagram Problem
Problem 4:

From building A to B there are three ways to go, and again from building B to A there are three ways. How many ways are there in total to go from building A to B and then return to building A from building B.


Let us see the tree diagram.

Example on Tree Diagram

Total number of leaves are 9. Hence, there are 9 ways to go from A to B and then return to A from B.