Modern digital technologies can be appropriately applied in the teaching of probability and statistics. Computer simulations represent an important part of application of digital technologies and they can be used to demonstrate various probability phenomena and patterns, analysis and evaluation of results of random experiments. Well-processed data in the form of summary tables and graphs can help in testing of students’ hypotheses or in guiding their considerations and decisions. In the article we focused on the description of prepared teaching materials and methodical guidelines for their use in the solving an interesting problem known as the “birthday paradox” in teaching of the probability properties.