将概率论知识点与社会重大事件结合分析的教学研究——以新冠肺炎病毒单检混检为例进行事件的独立性与互不相容性教学研究

Teaching Research on Combining Probability Theory with Social Major Event Analysis—Taking Single and Mixed Samples in COVID-19 Test as an Example to Conduct a Teaching Research on the Independence and Mutual Exclusive Events

摘要: 在概率论的学习中，随机事件的独立性和互不相容性占有十分重要的地位，它们是两个不同的概念，容易引起混淆并导致误解。但是，教师在教的过程中分析偏少，很少给出实际案例帮助学生理解；学生在学的过程中只记住了定义，在实际应用中容易混淆两者并导致错误计算。本文全面分析了两者之间的区别和联系，给出了若干命题，帮助学生多角度理解这些概念。最后以新型冠状病毒检测中的单检混检为例，说明在概率计算中运用加法公式和乘法公式时应该注意的问题，帮助学生更好地应用这些概念。

Abstract: The independence and exclusiveness of events plays an important role in probability theory, and they are two different concepts which are easy to cause confusion and misunderstanding. However, teachers have analyzed little and seldom give practical scenarios to help students understand in the teaching. Students only remember the definitions when learning, but confuse them and lead to wrong calculation in practical application. This literature comprehensively analyzes the differences and relations between them, and gives some propositions to help students understand these concepts from multiple perspectives. Finally, we take one sample and mixed samples test for COVID 19 as an example to explain the problems that should be paid attention to when applying addition formula and multiplication formula in probability calculation, which help students apply these concepts better.