SOLVING PRACTICAL PROBLEMS USING THE BERNOULLI SCHEME AND LIMIT THEOREMS FOR SEQUENCES OF INDEPENDENT TRIALS

In this article, we consider methods for solving practical problems related to calculating probabilities in a Bernoulli scheme of sequential independent trials. Particular attention is given to situations in which the direct application of Bernoulli's formula is difficult due to the large number of trials. The paper analyzes the conditions and demonstrates examples of using the Moivre-Laplace limit theorems (local and integral) and Poisson's theorem to obtain approximate probability values.本文探讨了序列独立试验伯努利（Bernoulli）概型下概率计算相关实际问题的求解方法。本文重点关注因试验次数过多而难以直接应用伯努利公式的场景。本文分析了相关应用条件，并辅以实例展示了如何运用棣莫弗-拉普拉斯（Moivre-Laplace）极限定理（局部型与积分型）以及泊松（Poisson）定理来求得近似概率值。