Question

In STAT 110, 73% of students earned at least a B on the part of the grade for attendance and participation. Of the students who earned at least a B on attendance and participation, 82% of those earned at least a B on the exams. Of the students who earned lower than a B on attendance and participation, only 48% earned at least a B on the exams. a) Draw an appropriate diagram (tree or Venn) for this problem, including all of the probabilities. b) What is the probability a randomly chosen student will have earned a B on the exams?

Answer 1

a)

b)

P(   atleast B attendence   ) =    0.73
P(   lower than B attendence   ) =    0.27

P(   Grade in exam   | atleast B attendence)=   0.82
P(   Grade in exam   | lower than B attendence)=   0.48

P(Grade in exam) = P(atleast B attendence) * P(Grade in exam| atleast B attendence) + P(lower than B attendence) *P(Grade in exam| lower than B attendence) =                                    0.73*0.82+0.27*0.48=               0.7282