Find the probability for the question below

Question: In a recent senatorial election, 52% of the voters in a certain district were registered as Democrats, 34% were registered as Republicans, and 14% were registered as Independents. The incumbent Democratic senator was reelected over her Republican and Independent opponents. Exit polls indicated that she gained 80% of the Democratic vote, 27% of the Republican vote, and 31% 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?

This question regards Bayes Theorem. Need help. Correct answer gets 10!

Let's say there are 1000 voters in the district, then we have
. . . . . . . . . . Dem . . . . . . Rep . . . . . Ind . . . Total
Overall: . . . . . 520 . . . . . . .340 . . . . . 140 . . 1000
Voted for X: ... 416 . . . . . . .91.8 . . . . . 43.4 . ... 551.2

P(Republican | voted for X) = 91.8 / 551.2 = 16.65 %

Or:
( .27 * .34 ) / ( .27 * .34 + .80 * .52 + .31 * .14 ) = 0.1665
Reps for X / All votes for X