Q:
      
      
         
            
At the university entrance exam, a candidate is admitted according to whether he has passed or failed the test. Of the candidates who are really capable, 80 % pass the test and of the incapable, 30 % pass the test. Given that 40 % of the candidates are really capable, then the proportion of the really capable students who can pass the test to the total students who can pass is about ?
         
       
      
      
      
          
      
      
          Answer & Explanation
         Answer: C) 16/25         
         
Explanation: If there are total 100 candidates, 
40 candidates are really capable and 
60 candidates are incapable.
Of the candidates who are really capable = 80% 
40*(80/100)=32 pass the test and
of the incapable= 30%
60*(30/100)=18 pass the test.
Total candidates who passed the test = 32+18 = 50
The proportion of the really capable students who can pass the test to the total students who can pass = 32/50 = 16/25.
       
      
      
      
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