Where two or three events occur, following on from each other, the various outcomes can be illustrated clearly on a tree diagram . This is particularly useful when later events depend in some way on the outcomes of previous events.

## Summary/Background

A

**tree diagram**is used to illustrate probabilities when two things happen by displaying outcomes and their probabilities on the branches. For example when two coins are spun, or if someone takes a counter from one bag followed by a counter from another bag, then the possibilities are shown on a tree diagram. The diagram shows all the possible outcomes. Usually the probability of each individual outcome is marked on each branch.## Software/Applets used on this page

## Glossary

### tree

A connected graph with no cycles.

### union

The union of two sets A and B is the set containing all the elements of A and B.

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic | Exam Year |
---|---|---|---|---|

AQA GCSE (9-1) Foundation (UK) | P: Probability | P8: Combined Events | Tree Diagrams | - |

CIE IGCSE (9-1) Maths (0626 UK) | 8 Probability | B8.5 Simple Combined Events | Tree Diagrams | - |

Edexcel GCSE (9-1) Foundation (UK) | P: Probability | P8: Combined Events | Tree Diagrams | - |

GCSE Higher (UK) | Probability | Probability | Tree diagrams | - |

OCR GCSE (9-1) Foundation (UK) | 11: Probability | 11.02d: Tree Diagrams | Tree Diagrams | - |

Universal (all site questions) | P | Probability | Tree diagrams | - |