Question

In a survey of $60$ people, it was found that $25$ people read newspaper $H$, $26$ read newspaper $T$, $26$ read newspaper $I$, $9$ read both $H$ and $I$, $11$ read both $H$ and $T$, $8$ read both $T$ and $I$, $3$ read all three newspapers. Which of the following statements is/are true? : The number of people who read exactly one newspaper is $30$. : Exactly one of the newspaper read is $n(H) + n(T) + n(I) - 2\\{n(H \cap I) + n(H \cap T) + n(T \cap T)\\}$ $+ 3n(H \cap T \cap I)$

• A. Only Statement-I
• B. Only Statement-II
• C. Both Statement-I and Statement-II
• D. Neither Statement-I nor Statement-II

Answer 1

Answer: (C)

Both Statement-I and Statement-II

Answer 2

Given, $n(H) = 25$, $n(T) = 26$, $n(I) = 26$, $n(H \cap I) = 9$, $n(H \cap T) = 11$, $n (T \cap I) = 8$ and $n(H \cap T \cap I) = 3$ $\therefore$ Number of people who read exactly one newspaper $= n(H) + n(T) + n(I) - 2\\{n(H \cap I) + n (H \cap I) + n(T \cap I)\\}$ $+ 3n(H \cap T \cap I)$ $= 25 + 26 + 26 - 2(9 + 11 + 8) + 3 \times 3 = 30$