10 freshman, 25% are sophomore, 16% are junior and the rest are senior. Among Ac

Question

10 freshman, 25% are sophomore, 16% are junior and the rest are senior. Among According to the record of the registrar's office at a state university, 35 % of the students are sophomores, juniors and seniors, the portion of students who live in the dormitory a the freshmen, 80%, 60%, 30% and 20%. [10 pts] are, respectively a. If a randomly selected student lives in the dormi freshman? itory, what is the probability that the student isa b. If a randomly selected student lives in the dormitory, what is the probability that the student is not a freshman?

Explanation / Answer

P(freshman) = 0.35

P(sophomore) = 0.25

P(junior) = 0.16

P(senior) = 1 - (0.35 + 0.25 + 0.16) = 0.24

P(live in dormitory | freshman) = 0.8

P(live in dormitory | sophomore) = 0.6

P(live in dormitory | junior) = 0.3

P(live in dormitory | senior) = 0.2

a) P(live in dormitory) = P(live in dormitory | freshman) * P(freshman) + P(live in dormitory | sophomore) * P(sophomore) + P(live in dormitory | junior) * P(junior) + P(live in dormitory | senior) * P(senior)

                                   = 0.8 * 0.35 + 0.6 * 0.25 + 0.3 * 0.16 + 0.2 * 0.24

                                   = 0.526

P(freshman | live in dormitory) = P(live in dormitory | freshman) * P(freshman) / P(live in dormitory)

                                                = 0.8 * 0.35 / 0.526

                                                = 0.5323

b) P(not freshman | live in dormitory) = 1 - P(freshman | live in dormitory) = 1 - 0.5323 = 0.4677

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