What Is a Tree Diagram in Mathematics?

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.

Understanding Tree Diagram in Mathematics

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. 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.

How Do Tree Diagrams Work?

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.

Example of a tree diagram.
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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.