43. This problem will present another proof of the Ballot Problem of Example 3.21.

(a) Argue that Pn,m = 1 - Ñ [A and  are tied at some point)

(b) Explain why P[A receives first vote and they are eventually tied)

= P[B receives first vote and they are eventually tied)

Hint: Any outcome in which they are eventually tied with A receiving the first vote corresponds to an outcome in which they are eventually tied with  receiving the first vote. Explain this correspondence.

(c) Argue that Pfeventually tied) = 2m/(n + ra), and conclude that Pn,m = (n - rri)/(n + m).