In a major athletics competition, an athlete has three attempts to clear a certain height. If he succeeds in his first or second attempt, he makes no other attempts on this height.

(i) Write down a suitable sample space Ω for this experiment and identify which elements of that space are included in the event E: the athlete clears the height in one of his three attempts.

(ii) Let Ei be the event that “the athlete makes a total of i attempts in this height,”

for i = 1, 2, 3. Identify the elements of each event Ei.

(iii) Express in terms of the events E1, E2, and E3 each of the following events:

A: the athlete fails in his first attempt;

B: the athlete fails in his first two attempts;

C: the athlete clears the height in his second attempt.

Can you do the same for the event E in Part (i)? If yes, explain how; otherwise, explain why not.