TABLE 4-8 (According to the record of the registrar\'s office at a state univers
ID: 3069775 • Letter: T
Question
TABLE 4-8 (According to the record of the registrar's office at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior, and the rest are senior. Among the freshmen, sophomores, juniors, and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30%, and 20%. ) 40. Referring to Table 4-8, what is the probability that a randomly selected student is a freshman who lives in a dormitory?
41. Referring to Table 4-8, what is the probability that a randomly selected student is a sophomore who does not live in a dormitory?
42. 130) Referring to Table 4-8, what is the probability that a randomly selected student is a junior who does not live in a dormitory?
43. Referring to Table 4-8, what is the probability that a randomly selected student is a junior or senior who lives in a dormitory?
44. Referring to Table 4-8, what percentage of the students live in a dormitory? 45. Referring to Table 4-8, what percentage of the students do not live in a dormitory?
46. Referring to Table 4-8, if a randomly selected student lives in the dormitory, what is the probability that the student is a freshman?
47. Referring to Table 4-8, if a randomly selected student does not live in the dormitory, what is the probability that the student is a junior or a senior?
Explanation / Answer
40) probability that a randomly selected student is a freshman who lives in a dormitory
=P(freshman)*P(Dormitary|freshman)=0.35*0.80=0.28
41)
probability that a randomly selected student is a sophomore who does not live in a dormitory
=P(sophomore )*P(not in dormitory|sophomore)=0.25*(1-0.6)=0.1
42)
probability that a randomly selected student is a junior who does not live in a dormitory
=0.16*(1-0.3)=0.112
43)
P(senior)=1-0.35-0.25-0.16 =0.24
probability that a randomly selected student is a junior or senior who lives in a dormitory
=0.16*0.3+0.24*0.2=0.096
44)percentage of the students live in a dormitory
=P(freshman)*P(Dormitary|freshman)+P(sophomore)*P(Dormitary|sophomore)+P(junir)*P(Dormitary|junior)+P(senior)*P(Dormitary|senior)
=0.35*0.8+0.25*0.6+0.16*0.3+0.24*0.2=0.526
45)
percentage of the students do not live in a dormitory =1-P(live in dormitory)=1-0.526=0.474
46)
probability that the student is a freshman given lives in the dormitory
=P(freshman)*P(Dormitary|freshman)/P(live in dormitory) =0.35*0.8/0.526 =0.5323
47)probability that the student is a junior or a senior given not live in dormitory
=(0.16*(1-0.3)+0.24*(1-0.2))/(1-0.526)=0.64135
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