Randomization and probabilistic approach in the algorithms development occupy prominent place.Due to limited computing resources and complexity many tasks in some cases it’s impossible to obtain accurate results or it’s too costly, so the results may contain some uncertainty. There are also cases when the indeterminacy of the algorithm is its advantage, for example in cryptography problems, or a useful characteristic: in simulations of processes containing undefined parameters.In this paper, we consider the basic concepts and statements concerning randomized algorithms for checking numbers for simplicity, we present the necessary theorems.