The evaluation of the probability of union of a large number of independent events requires several combinations involving the factorial and the use of high performance computers with several hours of processing. Bounds and simplifications on the probability of the union are useful in the analysis of stochastic problems across various areas including (but not limited to) systems reliability, biological systems, real-time fault-tolerant systems, probability theory, information theory and communications. We propose an approximation to evaluate the probability of the union of several independent events that uses the arithmetic mean of the probability of all of them. The approximate results are very close to, but larger than the exact values. The method allows a much smaller number of operations with a similar result and more simplicity.

翻译：评估大量独立事件的并集概率需要涉及阶乘的多种组合运算，并需借助高性能计算机进行数小时处理。在系统可靠性、生物系统、实时容错系统、概率论、信息论与通信等（但不限于）多个领域的随机问题分析中，对并集概率的界与简化具有重要价值。本文提出一种利用所有事件概率的算术均值来评估多个独立事件并集概率的近似方法。近似结果与精确值极为接近，但略大于精确值。该方法能以更少的运算量、更简洁的方式获得相近的结果。