Chapter 9.1, Problem 21E

Political Polls: Morris Polling conducted a poll 6 months before an election in a state in which a Democrat and a Republican were running for governor and found that $60\%$ of the voters intended to vote for the Republican and $40\%$ intended to vote for the Democrat. A poll conducted 3 months later found that $70\%$ of those who had earlier stated a preference for the Republican candidate still maintained that preference, whereas $30\%$ of these voters now preferred the Democratic candidate. Of those who had earlier stated a preference for the Democrat, $80\%$ still maintained that preference, whereas $20\%$ now preferred the Republican candidate.

$a.$ If the election were held at this time, who would win?

$b.$ Assuming that this trend continues, which candidate is expected to win the election?