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In probability theory
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expre ...
, a tree diagram may be used to represent a probability space
In probability theory, a probability space or a probability triple (\Omega, \mathcal, P) is a mathematical construct that provides a formal model of a random process or "experiment". For example, one can define a probability space which models ...
.
A tree diagram may represent a series of independent events
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes. Two events are independent, statistically independent, or stochastically independent if, informally speaking, the occurrence of ...
(such as a set of coin flips) or conditional probabilities
In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) is already known to have occurred. This particular method relies on ...
(such as drawing cards from a deck, without replacing the cards). Each node on the diagram represents an event
Event may refer to:
Gatherings of people
* Ceremony, an event of ritual significance, performed on a special occasion
* Convention (meeting), a gathering of individuals engaged in some common interest
* Event management, the organization of eve ...
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
A decision tree is a decision support system, decision support recursive partitioning structure that uses a Tree (graph theory), tree-like Causal model, model of decisions and their possible consequences, including probability, chance event ou ...
*Markov chain
In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally ...
Notes
References
*Charles Henry Brase, Corrinne Pellillo Brase: ''Understanding Basic Statistics''. Cengage Learning, 2012, , pp. 205–208online copy at Google
External links
*- examples and application
Experiment (probability theory) {{probability-stub