At a particular university, a study has shown that students who live on campus are more likely to have GPAs over 3.0 than students who do not. A freshman at this university is randomly selected at the beginning of the fall term. Define events A = {the student lives on campus}, and B = {the student has a GPA over 3.0 at the end of the fall term}. According to the housing office, P(A) = .80. Which statement is definitely true about P(B|A) based on this information?
A) P(B|A) = .80
B) P(B|A) is greater than P(B|not A)
C) P(B|A) is less than P(B|not A)
D) P(B|A) = P(B|not A)

Question

Quizplus · Accepted Answer

The study's finding that students who live on campus are more likely to have GPAs over 3.0 than those who do not directly implies that the probability of having a GPA over 3.0 given that a student lives on campus (P(B|A)) is greater than the probability of having a GPA over 3.0 given that a student does not live on campus (P(B|not A)).

At a Particular University, a Study Has Shown That Students