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. $50$
• B. $75$
• C. $125$
• D. $65$

Answer 1

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 $n\left(U\right)=a+b+c+d=400\cdots \left(1\right)$
$b+c=150,a+b=300,d=25$
$\Rightarrow (b+c)+(a+b)+d=475$
i.e., $a+2b+c+d=475\cdots \left(2\right)$
Subtracting $\left(1\right)$ from $\left(2\right)$, we get
$b=75$