75. This problem will present another proof of the ballot problem of Example 3.24.

(a) Argue that Pn,m = 1 − P{A and B 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 B receiving the first vote. Explain this correspondence.

(c) Argue that P{eventually tied} = 2m/(n + m), and conclude that Pn,m =

(n − m)/(n + m).