To find the probability distribution of \(X\), we consider the possible values of \(X\): 0, 1, or 2.

Case 1: \(X = 0\)

This means no 5s are chosen. There are 6 non-5 digits (1s and 3s) and 3 5s. The probability of choosing two non-5s is:

\(P(0) = \frac{6}{9} \times \frac{5}{8} = \frac{30}{72} = \frac{5}{12}\)

Case 2: \(X = 1\)

This means one 5 is chosen. From part (ii), \(P(1) = 0.5\).

Case 3: \(X = 2\)

This means two 5s are chosen. From part (i), \(P(2) = \frac{6}{72} = \frac{1}{12}\).

The probability distribution table is: