(i) The number of male students who do not play the piano is the sum of male students who play the guitar and the flute:

\(78 + 42 = 120.\)

The probability that a randomly chosen student is a male who does not play the piano is:

\(\frac{120}{300} = 0.4\).

(ii) To determine if the events are independent, we check if \(P(\text{male}) \times P(\text{not piano}) = P(\text{male} \cap \text{not piano})\).

The probability that a student is male is:

\(P(\text{male}) = \frac{160}{300}\).

The probability that a student does not play the piano is:

\(P(\text{not piano}) = \frac{225}{300}\).

Therefore,

\(P(\text{male}) \times P(\text{not piano}) = \frac{160}{300} \times \frac{225}{300} = \frac{8}{15} \times \frac{3}{4} = \frac{2}{5}\).

The probability that a student is male and does not play the piano is:

\(P(\text{male} \cap \text{not piano}) = \frac{120}{300} = \frac{2}{5}\).

Since \(P(\text{male}) \times P(\text{not piano}) = P(\text{male} \cap \text{not piano})\), the events are independent.