计算机辅助教学下分配问题的概率计算

Probability Calculation for Assignment Problems under Computer-Assisted Instruction

摘要: 《概率论与数理统计》中古典概型的计算是重难点，其中对物品进行分组的问题称为分配问题，本文给出了计算分配问题基本事件总数以及感兴趣事件含基本事件数量的公式。为进一步强化教学的可视化和验证环节，凸显计算机辅助教学的价值，文章引入蒙特卡罗模拟方法。这种“理论公式 + 计算机验证”的融合教学模式，在提升学生对分配问题精确建模的同时，培养了学生运用计算工具解决复杂概率问题的思维。教学实践表明，该方法能有效突破传统课堂中抽象公式推导的瓶颈，显著提升学生的学习兴趣和解决实际问题的信心。

Abstract: In Probability and Mathematical Statistics, the calculation of classical probability models is a key and challenging component. Among these, the problem of grouping objects is defined as the assignment problem. This paper provides formulas for calculating the total number of elementary events in assignment problems and the count of elementary events corresponding to the target event. To enhance visualization and validation in teaching and underscore the value of computer-assisted instruction, we integrate Monte Carlo simulation. The integrated teaching model of “theoretical formulation + computational verification” not only enhances students’ ability to precisely model allocation problems but also cultivates their computational thinking for solving complex probability-related challenges. Teaching practices demonstrate that this approach effectively overcomes the bottleneck of abstract formula derivation in traditional classrooms, significantly boosting students’ learning motivation and confidence in addressing real-world problems.