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In a class of 400 students, 150 are interested in doing a statistics project, 300 are interested in doing a machine learning project and 25 are not interested in doing either of the projects. Then the number of students who are interested in doing both the projects, is 
  1. 75
  2. 125
  3. 50
  4. 65


Solution

The correct option is A 75
Let M be the set of students interested in doing a machine learning project,
and S be the set of students interested in doing a statistics project.


Given n(U)=a+b+c+d=400     (1)
b+c=150, a+b=300, d=25 
(b+c)+(a+b)+d=475
i.e., a+2b+c+d=475     (2)
Subtracting (1) from (2), we get
b=75

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