An in-game tip says kids can inherit their kids skills.

Unfortunately, my approach of having a mom and dad who both mastered the same skill yielded a clutch of kids with no skills at all.

How exactly does skill inheritance work? Is it partly or mostly random?

//Moderators note: I removed the erroneous answers posted by another member. This is part of our effort to clean up the forum. //

To answer your question, with level 2 Culture, some (not all) children will be born with a small amount of skill in an area. This increases considerably with level 3.

Generally speaking, the child will inherit the mothers skill, and if both the mother and father are masters of a skill the child will inherit that skill.

However, most parents are skilled in more than one area, so that may explain why you're not getting the results you are expecting.