Question

A professor thinks students who live on campus are more likely to get As in the probability course. To check this theory, the professor combines the data from the past few years:

a. 600 students have taken the course,
b. 120 students have gotten As,
c. 200 students lived on campus,
d.80 students lived off campus and got As.
Does this data suggest that "getting an A" and "living on campus" are dependent or independent?

Answer 1

the data suggest that getting an "A" and "living on campus" are independent events

Explanation:

Since 120 students have gotten As and 80 students lived off campus and got As then the remaining 40 students that got As should be on campus.

For 2 events A and B , in order to be independent, they must satisfy

P(A∩B)=P(A)*P(B)

defining the event A= a student lived on campus, and event B= a student got A

P(A∩B)= 40/600= 1/15

P(A) = 200/600 = 1/3

P(B)= 120/600 = 1/5

since P(A∩B)=1/15 = 1/5*1/3 → the events A and B are independent