For purposes of making on-campus housing assignments, a college classifies its students as Priority A (seniors), Priority B (juniors), and Priority C (freshmen and sophomores). Of the students who choose to live on campus, 22% are seniors, 29% are juniors, and the rest are underclassmen. The most desirable dorm is the newly constructed Gold dorm, and 71% of the seniors elect to live there. 19% of the juniors also live there, along with only 5% of the freshmen and sophomores. What is the probability that a randomly selected resident of the Gold dorm is a senior? Show as much work as possible.