In a tennis tournament, 16 female players will compete for the title. In the first round of the tournament, the players will form randomly eight pairs and each pair will play a match. The eight winners of these matches will then form four new pairs. Each of these new pairs will play a match and the four winners will enter the semi-final round. There will be another draw to make two semi-final pairs; the two winners of the semi-final round will enter the final.

Amelia and Irène are two players who enter the tournament. Find the probability that they will meet

(i) in the first round;

(ii) in the second round;

(iii) in the final.