In the sample space of example (5.b) let us attribute to each point of (*) containing exactly k letters probability 1/2. (In other words, aa and bb carry probability, acb has probability, etc.)

(a) Show that the probabilities of the points of (*) add up to unity, whence the two points (**) receive proba- bility zero.

(b) Show that the probability that a wins is 14.

The probability of b winning is the same, and c has probability of winning.

(c) The proba- bility that no decision is reached at or before the kth turn (game) is 1/2-1.