(i) The probability of getting a green robot from one packet is \(\frac{1}{4}\) since there are four equally likely colours.

(ii) The probability that Nick gets his first green robot on the fifth packet means he does not get a green robot in the first four packets and then gets a green robot on the fifth. The probability of not getting a green robot in one packet is \(\frac{3}{4}\). Therefore, the probability is \(\left( \frac{3}{4} \right)^4 \times \frac{1}{4} = \frac{81}{1024} = 0.0791\).

(iii) The probability that the first four packets Amos opens all contain different coloured robots is calculated by considering the permutations of the four colours. The probability is \(\frac{1}{4} \times \frac{1}{4} \times \frac{1}{4} \times \frac{1}{4} \times 4! = \frac{3}{32}\).