These days, with the cost of a college education it is important to be able to graduate with a bachelor's degree in 4 years. The
National Association of Independent Colleges and Universities (NAICU) certainly would encourage students to attend independent schools. They provided the following information:(i) 20% of all college students attend private colleges and universities(ii) 55% of all college students graduate in 4 years(iii) 79% of students attending private colleges and universities graduate in 4 years.Based on the results of this study is "attending a private college or university" independent of "graduating in 4 years"?
This problem involves independence criteria for conditional probabilities.
The two events will be independent if P(A/B)=P(A) or P(B/A)=P(B)
Let us assumes that event A is for student attending private college and B is for student graduating in four years.
So we are given the following probabilities
P(A)=0.20
P(B)=0.55
P(B/A)=0.79
As we can see that P(B/A)≠P(B) so the events A and B are not independent.
So based on the above results we can say that "attending a private college or university" is not independent of "graduating in four years". Thus the two events "attending a private college or university" and "graduating in four years" are dependent.
