IT办公室的安全系统由10台计算机组成，其中4台正在运行。为了检查系统是否正常运行，官员检查了随机挑选的四台计算机(不更换)。如果检查的四台计算机中至少有三台正在运行，则认为该系统正常运行。用p表示系统被视为功能正常的概率。然后100p = _____________。
(A) 11.85答案： (A)
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