1. A statistics professor classifies his students according totheir grade point average (GPA) and their class rank. GPA is on a0.0 – 4.0 scale, and class rank is defined as the lower class (year1 and year 2) and the upper class (year 3 and year 4). One studentis selected at random.
| GPA | |
| Under 20 | 2.0 -3.0 | over 3.0 | |
| Lower Class (Year 1 and 2) | 0.05 | 0.20 | 0.10 | 0.35 |
| Upper Class (Year 3 and 4) | 0.10 | 0.35 | 0.20 | 0.65 |
| 0.15 | 0.55 | 0.30 | 1 |
a. Given that the student selected is in the upper class (year 3and 4), what is the probability that her GPA over 3.0?
b. What is the probability that the student is in the upperclass (year 3 and 4) or having a GPA over 3.0?
c. Are being in the upper class (year 3 and 4) and having a GPAover 3.0 independent? Prove statistically.
d. Are being in the upper class (year 3 and 4) and having a GPAover 3.0 mutually exclusive? Prove statistically.
