“Probable cause” in legal parlance is not the same as a statistical analysis. It’s a reasonable person thing NOT “what do we think probably happened” - but is the evidence enough to give rise to a reasonable suspicion that such-and-such crime has been committed.
And when it comes to granting cert, it is very clear from the petitions submitted to the Supreme Court what the issues are – at that point there are never any factual issues to be determined, only legal. So there is certainly room for debate, but it is never going to be about what’s “probable” – though you are right that an individual Justice’s vote on whether to grant cert might be based on considerations of probable outcome.
I agree with you that a math tutor would have made sense, but my sense was that the kid & parents were in denial at the time. The kid was in constant conflict throughout the school year with the Math II teacher over grades, but it seems like they were pretty much stuck on proving the teacher wrong rather than addressing whatever difficulties or deficiencies were giving rise to the weaker grades.
I’d point out that teachers sometimes have good reasons to be more accommodating of some students than others, simply because of the perceived ability or needs of the student. That is, a teacher might be a lot more forgiving of an athlete who is getting 100% on the quizzes and exams than a student who is doing C work. My son was able to convince his advanced level high school math teachers to waive homework requirements for him entirely, because he clearly understood the math and aced all the exams. So for him, the homework really was unneeded busy work. But he needed to demonstrate his ability first – I’m sure there is no way in the world those teachers would have agreed to the same sort of waiver for kids who were doing anything less than consistent A level work. I once got a D in high school math where I had 100% on all the exams… but had not bothered to turn in any of the homework, something my more rigid math teacher was unwilling to forgive.