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. Suppose the student does not live in the Gold dorm. What is the probability that the student is a junior? Round to three decimals.

Explanation / Answer

probabilty of freshman or sophomore =1-0.1-0.2=0.7

probabilty of freshmen or sophomore live in Gold Dorm =0.05

probabilty that student does not live in Gold Dorm =0.1*(1-0.6)+0.2*(1-0.15)+0.7*(1-0.05)=0.875

therefore probabilty that student is junior given does not live in Gold Dorm =0.7*(1-0.05)/0.875 =0.76

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