3 Suppose that in an election there are two candidates A and

(3) Suppose that in an election there are two candidates A and B. Candidate A receives n, while B receives m votes, n > m. What is the probability A is never behind in the count of votes if all orderings of the votes are equally likely?

Solution

Ok, after some research, I found that this is a replica of Bertrand\'s ballot theorem. This particular theorem has some nasty proofs and the answers differs with the numbers of votes, but the general formula in this case would be : (n - m) / (n+m), where n > m. Hope this helps. And since the top number would be smaller than the bottom number, you would get a decimal value and therefore a percent answer.