There are n voters in an upcoming election in a certain country, where n is a large, even number. There are two candidates: Candidate A (from the Unite Party) and Candidate B (from the Untie Party)....

There are n voters in an upcoming election in a certain country, where n is a large, even number. There are two candidates: Candidate A (from the Unite Party) and Candidate B (from the Untie Party). Let X be the number of people who vote for Candidate A. Suppose that each voter chooses randomly whom to vote for, independently and with equal probabilities. (a) Find an exact expression for the probability of a tie in the election (so the candidates end up with the same number of votes). (b) Use Stirling's approximation, which approximates the factorial function as'
n n n! c? N/27rt (—)
to find a simple approximation to the probability of a tie. Your answer should be of the form lAgn, with c a constant (which you should specify).