Algebraic structures are commonly used as a tool in treatments of various processes. But their exactness reduces the opportunity of their application in nondeterministic environment. On the other hand, probability theory and fuzzy logic do not provide convenient means for expressing the result of combining elements in order to produce new ones. Moreover, these theories are not developed to “measure" algebraic properties. Therefore, we propose a new concept which relies both on universal algebra and probability theory. We introduce probabilistic mappings, and by them we define the notion of a probabilistic algebra. Let A and B be non-empty sets, and let DB be the set of all probability distributions on B. A probabilistic mapping from A to B is a mapping h : A ! DB. Let A be a set, n 2 N, and let An = f(a1; a2; : : : ; an)j ai 2 A; i = 1; 2; : : : ; ng be the n-th power of A. Every probabilistic mapping from An to A is a probabilistic (n-ary) operation on A. A pair (A; F) of a set A and a family F of probabilistic operations on A is called a probabilistic algebra. When F = ff g has one binary operation, then the probabilistic algebra (A; f) is a probabilistic groupoid. “Ordinary" groupoids are just a special type of probabilistic ones. Basic properties of probabilistic groupoids and some classes of probabilistic groupoids (with units, commutative, associative, idempotent, with cancellation, with inverses, quasigroups, groups) are treated in this paper. Here we consider only the finite case