全概率公式及其应用摘要 全概率公式是概率论中的一个重要公式，它是解决复杂事件的一条行之有效的途径，是化繁为简解决复杂事件的概率计算的重要手段，它的根本作用就是将复杂事件的概率化简为求解多个简单事件概率之和.文中一方面对全概率公式的有关理论进行了介绍，并且探讨了全概率公式在流水线生产口罩、新型冠状病毒的核酸检测等方面的问题，给出了相应的一些有意义的结果 ,证明了全概率公式在经济、医疗等很多情况下可以进行运用，同时说明全概率公式在生活中渗透越来越深；另一方面对全概率公式进行推广，介绍了推广的全概率公式的理论知识，然后将其运用到生活中可能遇到的抓阄和摸球模型这一类的实际问题中，解决了这类复杂问题中事件的概率.通过这样的案例说明全概率公式可以应用到更复杂的生活实例中.关键词 全概率公式 复杂事件 应用 推广 完备事件组Law of Total Probability and Its ApplicationsAbscrat Law of total probability is an important formula in probability theory, it is an effective way to solve complex events, and it is an important means to simplify the probability calculation of complex events, its basic function is to simplify the probability of complex events to the sum of simple events. On the one hand, the paper introduces the theory of Law of total probability, and discusses the problems of Law of total probability in the production line of masks, nucleic acid detection of 2019-ncov, etc. , the results show that Law of total probability can be used in many situations, such as economy and medical treatment, and that Law of total probability is penetrating more and more deeply into people's life On the other hand, the paper generalizes the Law of Total Probability, introduces the theory of Law of total probability, and then applies it topractical problems such as the lottery and the ball model, solving the probability of an event in such a complex problem shows that Law of total probability can be applied to mor...
