Elementary Probability

Abstract

In this section we consider only finite sets; i.e., sets with finite number of elements. We denote the set M, consisting of the elements a₁, a₂..., a_n, bv the notation M = {a₁, a₂,..., a_n}. When the context is clear, we shall denote the elements a_i of M only by their indices; i.e., M = {1, 2,..., n}. The number of elements of the set M will be denoted by ν(M); hence, in the example above we have ν(M) = n. If ν(M) = 0, we say that M is an empty set and denote it by ∅. With each of two sets A and B we can associate two other sets, A ∪ B and A ∩ B called, respectively, the union (sum) and the intersection (product). The set A ∪ B consists of the elements belonging to at least one of the sets A and B. The set A ∩ B consists of the elements belonging both to A and B. For simplicity we shall write AB instead of A ∩ B. If A and B do not have any common elements (AB = ∅), we call them mutually exclusive or disjoint. Only in such a case we shall denote their union by A + B instead of A ∪ B. The symbol A + B should remind us that the sets A and B are disjoint.