Problem 1: Gerrymandering Suppose that among a population, some fraction p of the voters support Party A, and 1 -p support Party B. In an election of N voters, let X be the number of votes cast for Party A. . What is the distribution of X? . What is the probability that Party A wins power in the election, or ties? . Suppose an election is held with 303 votes cast, where the probability of Party A support is 51%. What is the probability that Party A wins power? Consider separating the population into three regions or districts of equal population, District 1, 2, 3, with relative fractions of Party A support p1, p2, P3. . What is the relationship between p1, p2, ps and p? . If n votes are cast in each district, what is the probability that Party A wins at least two districts and takes power