4. A, B, and C take turns in flipping a coin. The first one to get a head wins.

The sample space of this experiment can be defined by

$$S = \begin{Bmatrix} 1, 01, 001, 0001,.... \\ 0000... \end{Bmatrix} $$

(a) Interpret the sample space.

(b) Define the following events in terms of S:

(i) A wins = A.

(ii) B wins = B.

(iii) (A U B)c.

Assume that A flips first, then B, then C, then A, and so on.