1. An average of the most recent surveys of the American public’s party identification indicates that 45% of eligible voters identify themselves as Democrats, 45% of eligible voters identify themselves as Republicans, 8% of eligible voters identify themselves as Independents, and 2% of eligible voters identify themselves as members of a third party. The latest census indicates that 19% of the public lives in the Northeast, 23% of the public lives in the Midwest, 36% of the public lives in the South, and 22% of the public lives in the West. Assume that the distribution of partisans is uniform in all parts of the country. If you randomly select respondents to participate in a survey, what is the probability that (20 points): a. The first person you contact will be a Republican? b. The first person you contact will be either a Democrat or an Independent? c. The first two people you contact will be an Independent and a member of a third party (in that order)? d. The first person you contact will be a Democrat, given that you choose a member of one of the two major parties? e. The first person you contact will be a Republican living in the South? f. The first two people you contact will be a Democrat from the West and a Northeasterner (in no particular order)? g. The first person you contact will be a member of a third party, given that you do not select someone from the Midwest?

a. The probability of the first person you contact being a Republican is 45%. b. The probability of the first person you contact being either a Democrat or an Independent is the sum of their individual probabilities: 45% + 8% = 53%. c. The probability of the first two people you contact being an Independent and a member of a third party (in that order) is the product of their individual probabilities: 0.08 * 0.02 = 0.0016, or 0.16%. d. The probability of the first person you contact being a Democrat, given that you choose a member of one of the two major parties (i.e., a Democrat or a Republican) is the proportion of Democrats among the major party members, which is 45% / (45% + 45%) = 0.5, or 50%. e. The probability of the first person you contact being a Republican living in the South is the product of their individual probabilities: 0.45 * 0.36 = 0.162, or 16.2%. f. The probability of the first two people you contact being a Democrat from the West and a Northeasterner (in no particular order) is the product of their individual probabilities: (0.45 * 0.22) + (0.19 * 0.45) = 0.1985, or 19.85%. g. The probability of the first person you contact being a member of a third party, given that you do not select someone from the Midwest, is the probability of selecting someone from the Northeast, South, or West who is a member of a third party, divided by the probability of not selecting someone from the Midwest. The probability of selecting someone from the Northeast who is a member of a third party is 0.02 * 0.19 = 0.0038, the probability of selecting someone from the South who is a member of a third party is 0.02 * 0.36 = 0.0072, and the probability of selecting someone from the West who is a member of a third party is 0.02 * 0.22 = 0.0044. The probability of not selecting someone from the Midwest is 1 - 0.23 = 0.77. Therefore, the probability of the first person you contact being a member of a third party, given that you do not select someone from the Midwest, is (0.0038 + 0.0072 + 0.0044) / 0.77, or approximately 0.02, or 2%.