(iii) To determine if events \(R\) and \(S\) are independent, we check if \(P(R \cap S) = P(R) \times P(S)\).

Given: \(P(R) = 0.5\), \(P(S) = 0.4\), and \(P(R \cap S) = \frac{120}{720} = \frac{1}{6}\).

Calculate \(P(R) \times P(S) = 0.5 \times 0.4 = 0.2\).

Since \(P(R \cap S) = \frac{1}{6} \neq 0.2\), events \(R\) and \(S\) are not independent.

(iv) Events \(R\) and \(S\) are exclusive if \(P(R \cap S) = 0\). However, \(P(R \cap S) = \frac{1}{6} \neq 0\), indicating there is an overlap between \(R\) and \(S\) (e.g., the combination 3, 4, 4).

Therefore, events \(R\) and \(S\) are not exclusive.