Question

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.

Answer 1

The probability that a randomly selected resident of the Gold dorm is a senior is 0.1562

Explanation:

The given percentage of each class of student is presented as follows;

Priority A (seniors) = 22%, ∴ P(s) = 0.22

Priority B (juniors) = 29%, ∴ P(j) = 0.29

Priority C (freshmen and sophomores) = (100 - 22 - 29)% = 49%, ∴ P(fs) = 0.49

The percentage of the seniors that elect to live at the Gold dorm, = 71%, ∴ P(sG) = 0.71

The percentage of the juniors that live at the Gold dorm = 19%, ∴ P(jG) = 0.19

The percentage of the freshmen and sophomores that live in the Gold dorm = 5%, ∴ P(fsG) = 0.05

The probability that a randomly selected resident of the Gold dorm is a senior = P(s∩sG) = P(s) × P(sG)

∴ P(s∩sG) = 0.22 × 0.71 = 0.1562

Therefore;

The probability that a randomly selected resident of the Gold dorm is a senior = P(s∩sG) = 0.1562.