52% of students registered at College A for Fall 2006 Qtr intended to transfer.
34% of students registered at College B for Fall 2006 Qtr intended to transfer.
45% of students registered at AB District for Fall 2006 Qtr intended to transfer.
Are the events "attends College A" and "intends to transfer" independent? Show numerical justification.
Quite right. My mistake.
You have:
Pr(intend to transfer | College A) = 0.52.
Pr(intend to transfer | College B) = 0.34.
Pr(intend to transfer | District AB) = 0.45.
Clearly the probability of transfer is conditional on location. So the events "attends College A" and "intends to transfer" are NOT independent.
Why not just say the following:
There's not a snowball's chance in a really hot place that the events "attends College A" and "intends to transfer" are independent. This is because Pr(intend to transfer) depends on location:
Pr(intend to transfer | College A) (= 0.52) Pr(intend to transfer | College B) (= 0.34) Pr(intend to transfer | District AB) (= 0.45).