Consider an election with 2 candidates and c voters. Assume that candidate 1 gets 0. votes and candidate 2 gets b votes, with a, > b, a, + b = c, so that candidate 1 eventually wins the election. The votes are counted one by one in a uniformly random ordering, and we would like to keep a running tally of who is currently winning. (i) Denote by Sn the number of votes for candidate 1 minus the number of votes for candidate 2 after 12, votes have been counted. Dene Mn :2 C_n/ (c n) and show that (Mn)n is a martingale. (ii) Dene T := min{0 g n g c : Mn = 0}, and set T = c 1 if there is no n with Mn 2 O. Show that T is a stopping time. (iii) With the above ingredients, show that that the probability that candidate 1 is always ahead throughout the running tally is equal to if