The guardian’s religion/culture does not affect the education level at all. (Funnily enough, when you come of age, and if you attended university, there is a 2% chance to become a drunkard…) This all but guarantees the best education trait unless your child is really dumb. This means to get the best trait you only need to pass 3 of these checks. If you build a university and send your child to it, the game adds a flat +12 to the final education_variable. The same modifiers are applied to the failure chance if your child/guardian has negative education traits. A guardian with Shrewd also adds 5 to this modifier. If your guardian is a genius, this adds 15 to the success modifier (with intelligent and quick being 10/5, respectively). Intelligent and quick add 15 and 10, respectively.
Of course, as we add more modifiers to this, it will account for slightly less than 6% (when taking into account everything). Having a genius child adds 6% to the base chance each year to succeed the check and add 2 points to their education variable.
If your child is a genius, this adds 20 to the success modifier (which is 80/120 or 66%).
Not having a guardian at all also adds 20 this modifier.