大门|大门-CS-2014-（第2组）|问题11

IT办公室的安全系统由10台计算机组成，其中正好有4台在工作。为了检查系统是否正常工作，官员们检查了随机挑选的四台电脑（没有更换）。如果被检查的四台计算机中至少有三台在工作，则系统被视为正常工作。让系统被认为是功能性的概率用p表示。然后100p=____________________。 （A） 11.85 答复: （A） 说明：

Total ways to pick 4 computers = 10*9*8*7

Total ways that at least three computers are fine = 
        Total ways that all 4 are fine + Total ways any 3 are fine

Total ways that all 4 are fine = 4*3*2*1

Total ways three are fine = 1st is Not working and other 3 working + 
                            2nd is Not working and other 3 working + 
                            3rd is Not working and other 3 working + 
                            4th is Not working and other 3 working + 
                         = 6*4*3*2 + 4*6*3*2 + 4*3*6*2 + 4*3*2*6
                         = 6*4*3*2*4


The probability = Total ways that at least three computers are fine /  
                  Total ways to pick 4 computers 
                =  (4*3*2*1 + 6*4*3*2*4) / (10*9*8*7)
                = (4*3*2*25) / (10*9*8*7)
                = 11.9% 

这个问题的小测验