This article is written to share teaching ideas about using commonly available computer applications--a spreadsheet, "The Geometer's Sketchpad", and "Wolfram Alpha"--to explore three classic and historically significant problems from the probability theory. These ideas stem from the authors' work with prospective economists, mathematicians, and teachers. The historical contexts include the problem of the division of stakes (14th century), the problem of the Grand Duke of Tuscany (17th century), and the problem of co-primality of two natural numbers chosen at random (19th century). The suggested use of computers can be extended to other probability contexts to achieve at least two goals: to make complex mathematical ideas more accessible and to emphasize the importance of experimental evidence as a means of conceptual development in mathematics for all student populations.