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?

Answer 1

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