Question

According to a survey of $500$ people, $300$ preferred tea while $100$ preferred coffee. $50$ people preferred both tea and coffee. how many people didn't prefer any of the drinks?

• A. $350$
• B. $150$
• C. $400$
• D. None of the above

Answer 1

The correct option is B $150$

Let, $T$ be the set of people who preferred Tea and $C$ be the set of people who preferred Coffee.

Given : $n\left(T\right)=300,n\left(C\right)=100,n(T\cap C)=50andn\left(U\right)=500$
To find : No. of people who do not prefer any of drink $=n(T\cap C{)}^{\prime }$

We know,
$n(T\cup C)=n\left(T\right)+n\left(C\right)-n(T\cap C)$
So, $n(T\cup C)=300+100-50$
$=350$
We also know,
$n(T\cup C)+n(T\cup C{)}^{\prime }=n(U)$
$n(T\cup C{)}^{\prime }=500-350$
$=150$