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, 15% are seniors, 30% are juniors, and the rest
are underclassmen (freshmen and sophomores). The most desirable dorm is the newly
constructed Gold dorm, and 70% of the seniors elect to live there. 10% of the juniors also
live there, along with only 5% of the freshmen and sophomores. What is the probability
that a randomly selected student resides in the Gold Dorm?