(i) The probability of choosing exactly 2 paperback books is calculated using combinations. The number of ways to choose 2 paperback books from 6 is \(\binom{6}{2}\), and the number of ways to choose 2 hardback books from 2 is \(\binom{2}{2}\). The total number of ways to choose 4 books from 8 is \(\binom{8}{4}\).

Thus, the probability is:

\(P(\text{exactly 2}) = \frac{\binom{6}{2} \cdot \binom{2}{2}}{\binom{8}{4}} = \frac{15}{70} = \frac{3}{14}\)

(ii) The probability distribution table for X is:

(iii) Given \(E(X) = 3\), we find \(\text{Var}(X)\) using the formula \(\text{Var}(X) = \sum x^2 p - (E(X))^2\).

\(\text{Var}(X) = \frac{12}{14} + \frac{72}{14} + \frac{48}{14} - 3^2\)

\(= \frac{3}{7}\)