The University of Dar es salaam College of Engineering offers various four years degree programs. The students in this college participate in several after-lecture activities, which can be classified into three types: athletics, fine arts, and others. The following table gives the number of students participating in each of these types of activities by grade: 1st 2nd 3rd 4th Total Year Year Year Year Athletics Fine arts 150 160 140 150 600 100 90 120 125 435 Other 125 140 150 150 565 Total 375 390 410 425 1600 For the purpose of this example, we will assume that every student at the school is in exactly one of these after-school activities. Consider each of the following statements, and make sure that you see how each follows from the information in the table: 1. There are 160-second year students participating in athletics. 2. The number of senior students participating in fine arts activities is 125. 3. There are 435 students in fine arts activities. 4. The college of engineering has 410 middle-level students. 5. The total number of students is 1600. The principal at the college of engineering selects students at random and invites them to have lunch with him to discuss various issues that might be of concern to them. He feels that random selection will give him the greatest chance of hearing from a cross-section of the student body. Required: a) Find the probability that a randomly selected student is a senior athlete. Assume that each student is equally likely to be selected b) Now suppose that the principal's secretary records not only the student's name but also the student level. The secretary has indicated that the selected student is a senior. Does this information change our assessment of the likelihood that the selected student is an athlete?
The University of Dar es salaam College of Engineering offers various four years degree programs. The students in this college participate in several after-lecture activities, which can be classified into three types: athletics, fine arts, and others. The following table gives the number of students participating in each of these types of activities by grade: 1st 2nd 3rd 4th Total Year Year Year Year Athletics Fine arts 150 160 140 150 600 100 90 120 125 435 Other 125 140 150 150 565 Total 375 390 410 425 1600 For the purpose of this example, we will assume that every student at the school is in exactly one of these after-school activities. Consider each of the following statements, and make sure that you see how each follows from the information in the table: 1. There are 160-second year students participating in athletics. 2. The number of senior students participating in fine arts activities is 125. 3. There are 435 students in fine arts activities. 4. The college of engineering has 410 middle-level students. 5. The total number of students is 1600. The principal at the college of engineering selects students at random and invites them to have lunch with him to discuss various issues that might be of concern to them. He feels that random selection will give him the greatest chance of hearing from a cross-section of the student body. Required: a) Find the probability that a randomly selected student is a senior athlete. Assume that each student is equally likely to be selected b) Now suppose that the principal's secretary records not only the student's name but also the student level. The secretary has indicated that the selected student is a senior. Does this information change our assessment of the likelihood that the selected student is an athlete?
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Transcribed Image Text:The University of Dar es salaam College of Engineering offers various four years degree
programs. The students in this college participate in several after-lecture activities, which can
be classified into three types: athletics, fine arts, and others. The following table gives the
number of students participating in cach of these types of activities by grade:
2nd
Total
1st
Year
3rd
4th
Year
Year
Year
Athletics
150
160
140
150
600
Fine arts
100
90
120
125
435
Other
125
140
150
150
565
Total
375
390
410
425
1600
For the purpose of this example, we will assume that every student at the school is in exactly
one of these after-school activities. Consider each of the following statements, and make sure
that you see how each follows from the information in the table:
1. There are 160-second year students participating in athletics.
2. The number of senior students participating in fine arts activities is 125.
3. There are 435 students in fine arts activities.
4. The college of engineering has 410 middle-level students.
5. The total number of students is 1600.
The principal at the college of engineering selects students at random and invites them to have
lunch with him to discuss various issues that might be of concern to them. He feels that random
selection will give him the greatest chance of hearing from a cross-section of the student body.
Required:
a) Find the probability that a randomly selected student is a senior athlete. Assume that
each student is equally likely to be selected
b) Now suppose that the principal's secretary records not only the student's name but also
the student level. The secretary has indicated that the selected student is a senior. Does
this information change our assessment of the likelihood that the selected student is an
athlete?
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