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正在工作，则该系统被视为正常工作。让系统被认为是有功能的概率用 p 表示。那么 100p = ____________。
(一) 11.85答案：(一)
解释：
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% 这个问题的测验