Event (probability theory)

An event is a subset of a sample space, representing outcomes of interest. Its probability is determined by a probability measure on that space.

Sample space: The set of all possible outcomes of a random experiment or model. An event is defined as a subset of this set.
Complement (set theory): The elements of a specified universe that are not in a given subset. It represents the event that the original event does not occur.
Conditional probability: The probability of one event given that another event has occurred. It updates an event's probability under information represented by another event.
Measurable set: A set belonging to a sigma-algebra, on which a measure is defined. In probability spaces, measurable sets are precisely the events eligible for probabilities.
Outcome (probability): A single possible result represented in a probability model. An event groups together outcomes from this underlying set.
Union (set theory): The set containing every element that belongs to at least one of its sets. It represents occurrence of at least one among several events.
Independent events: Events whose occurrence does not change one another's probabilities, expressed by a product rule. Independence is a relation defined between events.
Nonmeasurable set: A subset excluded from a measure's domain because no consistent measure value is defined for it. It shows why not every subset of every sample space must be an event.
Probability measure: A function assigning probabilities to measurable sets while satisfying nonnegativity and normalization conditions. It assigns probabilities to events in the model.
Intersection (set theory): The set of elements shared by all sets in a collection. It represents simultaneous occurrence of the events involved.

Linked from 17 pages