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, 10% are seniors, 20% are juniors, and the rest are underclassmen. The most desirable dorm is the newly constructed Gold dorm, and 60% of the seniors elect to live there. 15% 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?

Answer 1

The probability that a randomly selected resident of the Gold dorm is a senior is 6%.

Step-by-step explanation:

To find the probability that a randomly selected resident of the Gold dorm is a senior, we need to consider the percentage of seniors who elect to live in the Gold dorm. We are given that 60% of the seniors choose to live in the Gold dorm. Let's calculate the probability:

P(Senior and Gold) = P(Gold given Senior) * P(Senior)

P(Senior and Gold) = 0.6 * 0.1 = 0.06

Therefore, the probability that a randomly selected resident of the Gold dorm is a senior is 0.06, or 6%.