Tree diagram (probability theory)

Tree diagram for events $A$ and $B$.

In probability theory, a tree diagram may be used to represent a probability space.

Each node on the diagram represents an event and is associated with the probability of that event. The root node represents the certain event and therefore has probability 1. Each set of sibling nodes represents an exclusive and exhaustive partition of the parent event.

Each branch is also associated with a probability, conditional on the parent event. The probability associated with a node is equal to the product of all branch probabilities ancestral to the node.

The sum of sibling node probabilities equals the parent node probability. The sum of node probabilities at the same hierarchical level equals 1.