Graduate students at the College on the River and in the Cloud received 10,000 c
ID: 3219315 • Letter: G
Question
Graduate students at the College on the River and in the Cloud received 10,000 course grades last semester, broken down in the Table below by which school of the university taught the course. The schools are Management, Computer Science, and Communication. It is rumored that grades are lower in Computer Science than in Management and social sciences, due to some very strict, old-school graders. Consider the two events
A = the grade comes from a Computer Science course
B = the grade is below a B (this includes a B-)
Grade Level
A
B
Below B
Total
Management
2142
1890
2268
6300
Computer Science
368
432
800
1600
Communication
882
630
588
2100
Total
3392
2952
3656
10000
a) What is the probability that a randomly selected student had a grade below a B? Show or explain how you obtain your answer. (6 pts.)
b) What is the probability that a randomly selected student from the Computer Science school had a grade below a B? Show or explain how you obtain your answer. (6 pts.)
A
B
Below B
Total
Management
2142
1890
2268
6300
Computer Science
368
432
800
1600
Communication
882
630
588
2100
Total
3392
2952
3656
10000
Explanation / Answer
(a)
Out of 10000 students, 3656 students have grade below B so the probability that a randomly selected student had a grade below a B is
P(below a B) = 3656 / 10000 = 0.3656
(b)
Out of 1600 computer science students, 368 has grade below a B so we have
P(below a B|computer science) = 368 / 1600 = 0.2300
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