For purposes of making on-campus housing assignments, a college classifies its s

Question

For purposes of making on-campus housing assignments, a college classifies its students as Priority A (seniors), Priority B (juniors), 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 freshmen and sophomores. What is the probability that a randomly selected student lives in the Gold dorm? Round to three decimals.

Explanation / Answer

We have

P(S) = 0.10, P(J) = 0.20 , P(F&S) = 0.70

P(GD/S) = 0.60, P(GD/F&S) = 0.60, P(GD/J) = 0.15

Now

P(G) = P(GD/S)*P(S)+P(GD/J)*P(J)+P(GD/F&S)*P(F&S)

P(G) = 0.60*0.10+0.15*0.20+0.05*0.70 = 0.125

So, correct answer is 0.125

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