Question

In a group of $70$ people, $37$ like coffee, $52$ like tea and each person like at least one of the two drinks. How many people like both coffee and tea?

Answer 1

Let event $A$ be the people who like coffee.

Let event $B$ be the people who like tea.

So, People liking one of the two $=A\cup B$

So people liking both $=A\cap B$

Given:$n\left(A\right)=37,n\left(B\right)=52$ and $n(A\cup B)=70$

$\Rightarrow n(A\cap B)=n\left(A\right)+n\left(B\right)-n(A\cup B)$

or, $n(A\cap B)=37+52-70=19$

So the required people who likes both $=19$