A statistics professor classifies his students according to their grade point average (GPA) and their class rank. GPA is on a 0.0-4.0 scale, and class rank is defined as the under class (freshmen and sophomores) and the upper class (juniors and seniors). One student is selected at random.

GPA Class Under 2.0 2.0 - 3.0 Over 3.0 Totals

Under 3 15 6 24 Upper 6 18 12 36 Total 9 33 18 60

A student is randomly selected.

a) (1 point) What is the probability that the selected student is in an upper class?

b) (1 point) What is the probability that the selected student is in an upper class and has

a GPA under 2.0 ?

c) (1 point) What is the probability that the selected student has a GPA under 2.0,

knowing that he is in an upper class?

d) (1 point) If the selected student has a GPA under 2.0, what is the probability that he is

in an upper class?

e) (2 points) Are the events "the selected student has a GPA under 2.0" and "the selected

student is in an upper class" independents?