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.