Tree diagram (probability theory)

Tree diagram for events A and B. Part of a series on statistics

Probability theory

* Probability axioms

* Probability space
* Sample space
* Elementary event
* Event
* Random variable
* Probability measure

* Complementary event
* Joint probability
* Marginal probability
* Conditional probability

* Independence
* Conditional independence
* Law of total probability
* Law of large numbers
* Bayes' theorem
* Boole's inequality

* Venn diagram
* Tree diagram

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

A tree diagram may represent a series of independent events (such as a set of coin flips) or conditional probabilities (such as drawing cards from a deck, without replacing the cards).[1] 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.

The probability associated with a node is the chance of that event occurring after the parent event occurs. The probability that the series of events leading to a particular node will occur is equal to the product of that node and its parents' probabilities.

## See also

* Decision tree
* Markov chain

## Notes

1. ↑ "Tree Diagrams". BBC GCSE Bitesize. BBC. p. 1,3. http://www.bbc.co.uk/schools/gcsebitesize/maths/statistics/probabilityhirev1.shtml. Retrieved 25 October 2013.

## References

* Charles Henry Brase, Corrinne Pellillo Brase: Understanding Basic Statistics. Cengage Learning, 2012, ISBN 9781133713890, pp. 205–208 (online copy at Google)

## External links

* tree diagrams \- examples and applications

Tree Diagrams

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