(i) To find the probability that the two digits chosen are equal, consider the digits 1, 3, and 5 in the number 113 333 555. The probabilities are:

\(P(1, 1) = \frac{2}{9} \times \frac{1}{8}\)

\(P(3, 3) = \frac{4}{9} \times \frac{3}{8}\)

\(P(5, 5) = \frac{3}{9} \times \frac{2}{8}\)

Summing these probabilities gives:

\(\frac{2}{9} \times \frac{1}{8} + \frac{4}{9} \times \frac{3}{8} + \frac{3}{9} \times \frac{2}{8} = \frac{5}{18}\)

(ii) To find the probability that one digit is a 5 and one digit is not a 5, consider:

\(P(5, \overline{5}) + P(\overline{5}, 5)\)

\(= \frac{3}{9} \times \frac{6}{8} + \frac{6}{9} \times \frac{3}{8} = \frac{36}{72} = \frac{1}{2}\)