通过三种不同方式求解全概率公式中的概率问题

Solving Probability Problems of the Total Probability Formula by Three Different Ways

摘要: 全概率公式是通过“取条件”求概率问题的一个非常实用的方法，其“取条件”本质上是对影响该事件的样本空间进行划分，而样本空间划分选取的合适与否直接影响到概率的计算。对于多次试验中可重复出现的某随机事件，其出现与其前出现事件有内在联系，那其前出现事件的所有可能结果就是样本空间的划分。对于这样的问题，如果能准确给出样本空间的划分就可以运用全概率公式解决，其可能涉及到通过等式求解，通过递推关系求解，通过差分方程求解。本文给出了这三种方式求解全概率公式的分析过程，并通过具体例子给出了其求解过程，帮助学生深刻理解全概率公式的求法并加强其在生活中的应用。

Abstract: The total probability formula is very practical to solve probability problems through “taking conditions”. The “taking condition” is to divide the sample space and whether it can be divided appropriately will affect the probability calculation. For a random event that can be repeated in multiple tests, its occurrence is inherently related to its previous events, so all possible results of the previous events are the division of sample space. In such a case, if the division of sample space can be accurately given, the total probability formula can be used to solve it, which may involve solving by equation, through recursive relation and difference equations. In this paper, the analysis of solving the total probability formula in these three ways is presented through the specific examples to help students deeply understand the total probability formula method and strengthen its application in life.