Suppose that in a certain Texas town, 70% of the voters are Republicans, 20% of the voters are Democrats, and 10% of the voters are neither. Suppose that 85% of the Democrats voted for Obama and 15% of the Democrats voted for McCain. Suppose that 75% of the Republicans voted for McCain and 25% of the Republicans voted for Obama. Suppose that 60% of those who are neither a Democrat nor a Republican voted for Obama and 40% of those who are neither a Democrat or a Republican voted for McCain.
(a) What is the probability that a randomly selected voter from this town is a Republican and voted for McCain?
(b) Use the Law of Total Probability to calculate the probability that a randomly selected voter from this town voted for Obama.
(c) Use Bayes' Rule to calculate the probability that someone who voted for Obama is a Democrat.