I think independent trials is not an obviously good assumption. Any properly designed major will have later courses build on earlier ones, so one might have pre

I think independent trials is not an obviously good assumption. Any properly designed major will have later courses build on earlier ones, so one might have predicted that performance in the first course was more predictive of GPA than SAT score (though this isn't the only model that would lead to such a prediction). I, for one, am surprised that it appears to be so independent.