全概率公式、贝叶斯公式的推广及其应用

Extension and Application of The Total Probability Formula and The Bayes Formula

本文在事件组A1 ,A2 ,…An互不相容且 nj=1 Aj= ;事件组B1 ,B2 ,… ,Bm中的Bi(i=1 ,2 ,… ,m)只能与事件A1 ,A2 ,… ,An之一同时发生的条件下 ,得出事件Bi(i=1 ,2 ,… ,m)发生的概率的矩阵表达式—全概率公式的矩阵表示。另外还给出了在事件Bi(i=1 ,2 ,… ,m)发生的条件下事件A1 ,A2 ,…

? A group of incompatible events A 1,A 2,...,A n,wich satisfiesnj=1A j=,and B i(i=1,2,...,m)in the events group B 1,B 2,...,B m occurs simultaneously with one of events A 1,A 2,...,A n,the matrix expression of the probability of event B i(i=1,2,...,m)is given ,i.e.the matrix expression of total probability is given in this paper.Besides,under the conditions of the occurrence of event B i(i=1,2,...,m),the matrix expression of the probability of events A 1,A 2,...,A n is also given,this is matrix expression of B formula. 〔