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Question

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

A
50
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B
75
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C
125
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D
65
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Solution

The correct option is B 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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