几何概型的联系概率(复概率)与概率的补数定理

摘要

为研究等可能随机试验结果为无穷多时的联系概率计算和应用,借助简单的“均匀投针”随机试验,导出几何概型的联系概率(复概率).该联系概率中的主概率和伴随概率依次对应于主事件的大数概率(主概率)和主事件的即或概率(伴随事件的大数概率).在此基础上给出 了随机事件的表现定理和概率的补数定理,利用后者可以在已知一个随机事件概率的基础上方便地得到该事件的联系概率.通过实例说明了几何概型的联系概率与古典概型的联系概率具有同样的形式和性质.%In order to research the calculation and application of contact probability when the result of equally likely random trial is infinite, the researcher utilized the simple " uniform needle" random test to derive contact probability (complex probability) of geometry probability. The main probability and the concomitant probability of the contact probability respectively correspond to the great number probability ( main probability) of the main event and the even if probability (great number probability of concomitant event) of the main event. And on this basis, the representation theorem of the random event and complement number theorem of probability were provided in the study. The complement number theorem was used to conveniently find the contact probability of the event based on the premise of knowing the probability of a random event. The results illustrated that the contact probability of geometry probability had the same form and property with the contact probability of typical probability.