ABSTRACT 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.

中文翻译：

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用现代数字工具教授经典概率问题

摘要本文旨在分享有关使用常见的计算机应用程序（电子表格，Geometer的画板和Wolfram Alpha）的教学思想，以探讨来自概率论的三个经典且具有历史意义的问题。这些想法源于作者与准经济学家，数学家和教师的合作。历史背景包括股权分配问题（14世纪），托斯卡纳大公国问题（17世纪）以及随机选择的两个自然数的共素性问题（19世纪）。建议将计算机的使用扩展到其他概率环境，以至少实现两个目标：