(i) The number of red or silver cars manufactured in Korea is \(34 + 30 = 64\). The probability is \(\frac{64}{250} = 0.256\).

(ii) The number of cars not manufactured in Japan is \(250 - (26 + 22 + 12) = 190\). The probability is \(\frac{190}{250} = 0.76\).

(iii) Calculate \(P(X)\), \(P(Y)\), and \(P(X \cap Y)\):

\(P(X) = \frac{80}{250} = \frac{8}{25}\)

\(P(Y) = \frac{100}{250} = \frac{2}{5}\)

\(P(X \cap Y) = \frac{32}{250} = \frac{16}{125}\)

Check independence: \(P(X) \times P(Y) = \frac{8}{25} \times \frac{2}{5} = \frac{16}{125}\)

Since \(P(X) \times P(Y) = P(X \cap Y)\), events X and Y are independent.