The paper concerns discrete transformations of Boolean random variables, i.e. random variables which have only two values 0 and 1, with rational probabilities of values. By a discrete transformation of Boolean random variables we mean a Boolean random variable, the value of which is the value of an arbitrary Boolean function whose variables values are the values of the independent initial random variables. The closure of a set of probabilities is the set of probabilities of value 1 for all random variables obtained by discrete transformations of Boolean random variables whose probabilities of value 1 belong to the initial set of probabilities. A set of probabilities is closed if it coincides with its closure. In the paper all closed sets of rational probabilities are described.

Boolean random variables, rational probabilities, closed class

Mathematical problems and theory of numerical methods