Question

In a certain town, 40% of people have brown hair, 30% of people have brown eyes and 12% have both brown hair and brown eyes. How many people in town have neither brown hair nor brown eyes ?

Accepted Answer

D. Let $A$ be the set of people with brown hair and $B$ be the set of people with brown eyes. $P(A) = 40\%$, $P(B) = 30\%$, $P(A \cap B) = 12\%$. $P(A \cup B) = P(A) + P(B) - P(A \cap B) = 40\% + 30\% - 12\% = 58\%$. Percentage of people having neither = $100\% - 58\% = 42\%$.

Venn diagram of features

Explanation

Practise this under exam conditions