设总人数为100人,就共做了500道题;
5个题做对的人数分别是81、91、85、79、74,
则做对的总题数为:81+91+85+79+74=410(题),
错题数为500-410=90(题),
为找到及格率的最小值,就使得错题都是集中到三道题里。
90÷3=30(题),错三题的人为30人.
则及格率为:
(100-30)/100×100%=70%;
及格率至少为70%.
及格率最差的情况是及格的都是对5题,不及格都是对2题
所以明显,最差是74%
做对1、2、3、4、5题的分别占参加考试人数的81%,91%,85%,79%,74%,
那么做错1、2、3、4、5题的分别占参加考试人数的19%,9%,15%,21%,26%,
一道未对:19%×9%×15%×21%×26%=0.000140049
仅对一道:81%×9%×15%×21%×26%
+19%×91%×15%×21%×26%
+19%×9%×85%×21%×26%
+19%×9%×15%×79%×26%
+19%×9%×15%×21%×74%
=0.000597051+0.001416051+0.000793611+0.000526851+0.000398601
=0.003732165
仅对两道:81%×91%×15%×21%×26%
+81%×9%×85%×21%×26%
+81%×9%×15%×79%×26%
+81%×9%×15%×21%×74%
+19%×91%×85%×21%×26%
+19%×91%×15%×79%×26%
+19%×91%×15%×21%×74%
+19%×9%×85%×79%×26%
+19%×9%×85%×21%×74%
+19%×9%×15%×79%×74%
=0.006036849+0.003383289+0.002246049+0.001699299
+0.008024289+0.005327049+0.004030299
+0.002985489+0.002258739
+0.001499499
=0.03749085
及格率=1-不及格率
即及格率=1-0.000140049-0.003732165-0.03749085=0.958636936
所以及格率约为0.9586