Question:
A survey shows that 76% of the Indians like oranges, whereas 62% like bananas. What percentage of the Indians like both oranges and bananas?
Solution:
Let A & B denote the sets of the Indians who like oranges & bananas, respectively.
Given :
$n(A)=76 \%$
$n(B)=62 \%$
$n(A \cup B)=100 \%$
$n(A \cap B)=?$
We know :
$n(A \cup B)=n(A)+n(B)-n(A \cap B)$
$\Rightarrow 100=76+62-n(A \cap B)$
$\Rightarrow n(A \cap B)=38$
Therefore, $38 \%$ of the Indians like both oranges \& bananas.