Tree Diagram

Tree Diagram

Investopedia / Mira Norian

What Is a Tree Diagram?

A tree diagram is a tool in the fields of general mathematics, probability, and statistics that helps calculate the number of possible outcomes of an event or problem, and to cite those potential outcomes in an organized way.

Tree diagrams, also known as probability trees or decision trees, are quite versatile and may be useful in many fields, including finance.

Key Takeaways

  • A tree diagram is a tool in the fields of general mathematics, probability, and statistics that helps calculate the number of possible outcomes.
  • Tree diagrams are also known as probability trees or decision trees that aid the user in probability calculations.
  • A tree diagram lets a user start at a single point and make mutually exclusive decisions or experience mutually exclusive events to follow a path down the branches of the tree.
  • Tree diagrams combine the probabilities, decisions, costs, and payouts of a decision and provide a strategic answer.
  • The diagram starts at a single node, with branches emanating to additional nodes, which represent mutually exclusive decisions or events.

Understanding a Tree Diagram

A tree diagram lets a user start at a single point and make mutually exclusive decisions or experience mutually exclusive events to follow a path down the branches of the tree. Using a tree diagram is simple once you assign the appropriate values to each node.

Chance nodes, representing a possible outcome, must be assigned a probability. Decision nodes ask a question and must be followed by answer nodes, such as "yes" or "no." Often, a value will be associated with a node, such as a cost or a payout.

Today, there are a variety of online programs that allow users to create and use tree diagrams rather than having to draw them out by hand.

Tree diagrams combine the probabilities, decisions, costs, and payouts of a decision and provide a strategic answer. In finance, we can model the price of a put or call option using a decision tree given the price of the underlying security at a given point in time.

Tree Diagrams in Use

The idea behind a tree diagram is to start on the left with the whole thing, or one. Every time several possible outcomes exist the probability in that branch splits off into a smaller branch for each outcome.

The diagram starts at a single node, with branches emanating to additional nodes, which represent mutually exclusive decisions or events. In the diagram below, the analysis will begin at the first blank node. A decision or event will then lead to node A or B. From these secondary nodes, additional decisions or events will occur leading to the third level of nodes until a conclusion is reached.

Tree Diagram
Image by Julie Bang © Investopedia 2020

Additional Uses

In addition to mathematics, tree diagrams are used in strategic decision-making, company valuations, or probability calculations. Tree diagrams combine the probabilities, decisions, costs, and payouts of a decision and provide a strategic answer. In finance, we can model the price of a put or call option using a decision tree given the price of the underlying security at a given point in time.

Increasingly, decision trees are used in fintech algorithm design and user experience in fintech apps. One use case of decision trees would be how to set a suitable investment strategy for a new user of a robo-advisor based on an onboarding questionnaire.

How Can I Make a Tree Diagram for Probability?

To make a tree diagram for probability, branches need to be created with the probability on the branch and the outcome at the end of the branch. One needs to multiply continuously along the branches and then add the columns. The probabilities must add up to one.

Where Can I Create a Tree Diagram?

A tree diagram can be created in many ways, even with just a pencil and paper. Today, with a variety of Internet tools and programs, individuals can create tree diagrams with diagramming programs, such as Lucidchart and Edraw Max.

How Do I Make a Tree Diagram Online?

You can make a tree diagram online by using a variety of online charting and diagramming tools, such as Lucidchart and Edraw Max.

How Can I Make a Tree Diagram in Excel?

To make a tree diagram in Excel you will need to utilize third-party diagramming tools, such as Lucidchart that allows you to create a tree diagram in Excel. These are known as add-ins to the program.