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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.
\[\text{ Given }: \]
\[n\left( A \right) = 76 % \]
\[n\left( B \right) = 62 % \]
\[n\left( A \cup B \right) = 100 % \]
\[n\left( A \cap B \right) = ?\]
\[ \text{ We know }: \]
\[n\left( A \cup B \right) = n\left( A \right) + n\left( B \right) - n\left( A \cap B \right)\]
\[ \Rightarrow 100 = 76 + 62 - n\left( A \cap B \right)\]
\[ \Rightarrow n\left( A \cap B \right) = 38\]
\[\text{ Therefore, 38 % of the Indians like both oranges & bananas } .\]
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