(i) To find the probability that a student prefers swimming, we sum the number of students who prefer swimming and divide by the total number of students.

The total number of students who prefer swimming is \(104 + 31 = 135\).

The probability is \(\frac{135}{400} = 0.3375\).

(ii) To determine if the events are independent, we check if \(P(M \cap S) = P(M) \times P(S)\).

\(P(M) = \frac{180}{400} = 0.45\)

\(P(S) = \frac{135}{400} = 0.3375\)

\(P(M \cap S) = \frac{31}{400} = 0.0775\)

Calculate \(P(M) \times P(S) = 0.45 \times 0.3375 = 0.151875\)

Since \(0.151875 \neq 0.0775\), the events are not independent.