Consider the GPA of students in a private liberal arts colle

Consider the GPA of students in a private liberal arts college. In this college, there are 30% freshmen, 27% sophomores, 22% juniors and 21% seniors. If a student is a freshman (resp. sophomore, junior and senior), the probability of getting 3.5 or above is 15% (resp. 20%, 18%, and 18%). Now a student is selected at random in the college.

a) What’s the probability that a student’s GPA is 3.5 or above?
b) If a student’s GPA is 3.5 or above, what’s the probability that he/she is a sophomore?
c) If a student is either sophomore or junior and his/her GPA is 3.5 or above, what’s the probability that this student is a sophomore?

Solution