1. ## Independent probability?

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.

2. Originally Posted by Myung
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.
More information is needed. Please post the entire question, exactly as it's written wherever you got it from.

3. That is the whole question, in my book.

4. Originally Posted by Myung
That is the whole question, in my book.
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.

5. Isn't that just inferencing or does that count as numerical justification? I agree that the problem is poorly worded, my book is made by some of the teachers at my college so it is not exactly professionally done.

6. Originally Posted by Myung
Isn't that just inferencing or does that count as numerical justification? I agree that the problem is poorly worded, my book is made by some of the teachers at my college so it is not exactly professionally done.
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) $\displaystyle \neq$ Pr(intend to transfer | College B) (= 0.34) $\displaystyle \neq$ Pr(intend to transfer | District AB) (= 0.45).