(i) The probability of a single die landing on a green face is \(\frac{1}{4} = 0.25\). The probability of a die not landing on a green face is \(1 - 0.25 = 0.75\).

We use the binomial probability formula: \(P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}\).

For 4 dice landing on a green face, \(n = 5\), \(k = 4\), \(p = 0.25\):

\(P(X = 4) = \binom{5}{4} (0.25)^4 (0.75)^1\)

\(= 5 \times (0.25)^4 \times 0.75\)

\(= 5 \times 0.00390625 \times 0.75\)

\(= 0.0146484375\)

Rounding to 4 decimal places gives \(0.0146\).

(ii) The probability distribution of \(X\) is calculated using the binomial formula for each value of \(X\) from 0 to 5: