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[en] We propose an analytical solution to the on–off problem within the framework of Bayesian statistics. Both the statistical significance for the discovery of new phenomena and credible intervals on model parameters are presented in a consistent way. We use a large enough family of prior distributions of relevant parameters. The proposed analysis is designed to provide Bayesian solutions that can be used for any number of observed on–off events, including zero. The procedure is checked using Monte Carlo simulations. The usefulness of the method is demonstrated on examples from γ-ray astronomy.