Tree Diagrams

A tree diagram can be used in many disciplines for many different things. When it comes to probability, a tree diagram is used illustrates all the possible outcomes from an experiment (sample space). It can also be used to help determine the probability of individual outcomes within the sample space. It consists of arcs and nodes and each branch of the tree represents a possible outcome of one event. I can personally remember using tree diagrams in school when dealing with probability and found them very helpful because they allow you to better visualize and organize the problem you are working on. Many students will better understand probability and the problem that they are working with if they are able to have a visual representation in front of them. It is for this reason that I feel tree diagrams have a valid place in teaching probability to primary/elementary children. The following are sample probability problems that can be figured out through the use of a tree diagram:

1. Show the sample space for tossing one penny and rolling one die. (H = heads, T = tails)

By following the different paths in the tree diagram, you can arrive at the sample space which is { H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6 }. The probability of each of these outcomes is 1/2 x 1/6 = 1/12.


2. A family has three children. How many outcomes are in the sample space that indicates the sex of the children? Assume that the probability of male (M) and the probability of female (F) are each 1/2.

There are 8 outcomes in the sample space. The probability of each outcome is
1/2 x 1/2 x 1/2 = 1/8.

I also found a web site that provides some great probability problems that involve the use of tree diagrams that students could use for practice. Have a look!
Practice Page

The following are references used while creating this blog:

Lesson Plans: Tree Diagrams

Tiscali.Reference: Tree Diagram

Thanks!