The Ballot Problem In an election candidate A receives n vot

(The Ballot Problem) In an election, candidate A receives n votes, and candidate B receives m votes where n > m. Assume that in the count of votes, all orderings are equally likely.

In the ballot problem, compute

P ({A is never behind}) by using result of the first vote.

Solution

see every number has equal probability of having a number bigger and smaller then it.

P( A is never behind) this we have to find, it is given that n>m and a got n votes on whole.

in counting of votes two scenario are possible either A is winning or B is winning

since we have to find that p( a is never behind) = 1/2 ( according to the scenario decribed above)