According to the record of the registers office at a state university, 35% of th

Question

According to the record of the registers office at a state university, 35% of the students are freshman, 25% are sophomores, 16% are junior and the rest are senior. Among the freshman, sophomores, juniors and seniors, the portion who live in the dormitory are, respectively, 80%, 60%, 30%, and 20%.
What percentage of the students DO NOT live in a dormitory? According to the record of the registers office at a state university, 35% of the students are freshman, 25% are sophomores, 16% are junior and the rest are senior. Among the freshman, sophomores, juniors and seniors, the portion who live in the dormitory are, respectively, 80%, 60%, 30%, and 20%.
What percentage of the students DO NOT live in a dormitory?
What percentage of the students DO NOT live in a dormitory?

Explanation / Answer

P(freshman)=0.35, P(dormitory| freshman)=0.8

P(sophomore)=0.25 , P(dormitory | sophomore)=0.6

P(junior)=0.16, P(dormitory | junior)=0.3

P(senior)=1-(0.35+0.25+0.16)=0.24 , P(dormitory | senior)=0.2

Thus , P(dormitory)=P(dormitory| freshman)*P(freshman) +P(dormitory | sophomore)*P(sophomore) +P(dormitory | junior)*P(junior) +P(dormitory | senior)*P(senior)

=0.8*0.35+0.6*0.25+0.3+0.2*0.24 =0.778

P(do not live in dormitory)=1-0.778=0.222

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