This problem will present another proof of the ballot problem of Example 3.31.

(a) Argue that

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).

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Pn.m=1P{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}