Probemenge

Probemenge is a term used in some educational and theoretical contexts to denote a discrete probability model consisting of a finite set of events together with an associated probability measure. In this sense, a Probemenge is defined by a finite set X of events and a probability function p: X → [0,1] such that the sum of p(x) over all x in X equals 1. The Probemenge thus represents a discrete probability distribution over the events in X and supports standard probability calculations for unions, intersections, and conditional events.

Origin and usage: The term appears in a subset of European didactic resources as a simple, intuitive label for teaching basic probability without introducing random variables. In this usage, individual outcomes or events are treated as the fundamental units, each assigned a likelihood by p.

Formal properties: For any x in X, 0 ≤ p(x) ≤ 1 and ∑_{x∈X} p(x) = 1. If A and B are disjoint subsets of X, p(A ∪ B) = p(A) + p(B). Conditional probability is defined as p(A|B) = p(A ∩ B) / p(B) when p(B) > 0. Independence between events can be defined analogously via p(A ∩ B) = p(A)p(B).

Example and applications: A Probemenge on {A, B, C} with p(A)=0.2, p(B)=0.5, p(C)=0.3 models a simple three-outcome scenario, such as a finite set of survey responses or a discrete die-throw result. It is useful for illustrating core ideas in probability and as a stepping stone to more advanced concepts.

See also: Probability distribution, Probability mass function, Discrete random variable.