An upper-level math course is open to both udergraduate students and graduate students. THe table below gives the perfomance of the two level of students in the class last semester on the final exam:

capellitad9 2022-07-15 Answered
An upper-level math course is open to both udergraduate students and graduate students. THe table below gives the perfomance of the two level of students in the class last semester on the final exam:
Score, S, on Final Exam S < 70 70 S < 80 80 S < 90 90 S 100 Total Undergraduate 16 14 17 3 50 Graduae 4 10 19 7 40 Total 20 24 36 10 90
1) Find the probability that a student scored 80 or above and was a graduate student
2) Given that a student scored below 80, find the probability that the student was a graduate student
3) Find the probability that an undergraduate student scored 90 or above
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Answers (1)

Julianna Bell
Answered 2022-07-16 Author has 19 answers
Step 1
Event A = student score 80 and wus a graduate studebt. Because, there are total 46 student which score 80 or more but among thse 46 students 26(19+7) students are graduate
n ( A ) = 26 P ( A ) = n ( A ) n ( S ) = 26 90 = 0.288888 0.2889
Step 2
2) Event B = student score below 80
n ( B ) = 20 + 24 = 44 P ( B ) = n ( B ) n ( S ) = 44 90 = 0.488888
Event A = student is graduate student
( A B ) = student is graduate and score below 80
n ( A B ) = 10 + 4 = 14 P ( A B ) = n ( A B ) n ( S ) = 14 90 = 0.155555 P ( student is graduate | student score is below 80 ) P ( A | B ) = P ( A B ) P ( B ) = 0.155555 0.488888 = 0.318181 P ( A | B ) 0.3182
Step 3
3) Event c = undergraduate student score 90 or above
n ( c ) = 3 P ( c ) = n ( c ) n ( s ) = 3 90 = 0.3333
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