I'm a first time poster to this message board and a newbie to logistic regression.

Background: I conducted a logistic regression using enrolled in college as the dependent variable and passing a high school exit exam as the dependent variable (both are binary). My initial question was about the likelihood of being enrolled in college having passed this exam. One thing to note, however, is that not passing the exam does not exclude students from entering college.

So the school district data look like this...

Not passed, enrolled=661
Not passed, not enrolled=401

Passed, enrolled=221
Passed, not enrolled=30

I ran the analysis, got the intercept (.499) and b coefficient (1.497), and computed the probability of being in the "Passed" group as .88. Next, I computed the probability of being in the "Not Passed" group, and I get .62.

I'm confused by the findings. My question for the forum is about the interpretation of these findings. What does it mean that passing and not passing is predictive of college enrollment? Is it common that both "sides" of an independent variable (the 0 and the 1) are predictive of group membership in the dependent variable?
Thanks.