In a recent senatorial election, 47% of the voters in a certain district were registered as Democrats, 36% were registered as Republicans, and 17% were registered as Independents. The incumbent Democratic senator was reelected over her Republican and Independent opponents. Exit polls indicated that she gained 82% of the Democratic vote, 22% of the Republican vote, and 26% of the Independent vote. Assuming that the exit poll is accurate, what is the probability that a vote for the incumbent was cast by a registered Republican
+23246 47% of the voters were Democrats; she received 82% of this vote: 0,47 x 0.82 = 38.54%
36% of the voters were Republicans; she received 22% of this vote: 0.36 x 0.22 = 7.92%
17% of the voters were Independents; she recieved 26% of this vote: 0.17 x 0.26 = 4.42%
Adding these together, we see that she received 50.88% of the vote.
The Republican share was 7.92 / 50.88 = 15.57%.
Therefore, the probability that a vote for the incumbent is 0.1557.
