Definition
Tree diagram
A tree diagram branches step by step so each complete path shows one possible sequence or outcome.
What it means
Start at the left. Draw one branch for every possible first result. From each of those, draw every possible next result. Follow any path from start to finish to read one outcome. When every branch is included, the endpoints show the whole sample space.
Remember it
Every fork is a step; every full path is one outcome.
Example
For two coin tosses, the first toss branches to H and T. Each branch then splits again to H and T. The four complete paths are HH, HT, TH, and TT.
Watch for
A drawing of a tree or a family tree is not this mathematical representation. A probability tree is a tree diagram whose branches also carry probabilities.
Common mix-up
Do not merge HT and TH: they use the same letters but record different orders.
Exact meaning
A tree diagram is a branching representation of successive choices or events. Each branch shows one option at a step, and each complete path from the start to an endpoint represents one distinct sequence or outcome.