After struggling to solve a math problem, you suddenly see the solution. for no apparent reason, the method for solving the problem just came to your mind. you have experienced:

insight

Explanation:

When you have an insight, you have a feeling or emotion or thought that helps you to know something essential about a person or thing. ... When you gain insight, you are using your intuition, or sixth sense. Insight is formed from the prefix in- plus the English word sight, so this word literally means seeing inward.

answer; /// (a) and (b) ; /// but i believe the correct answer is ; /apart from fines and jail time, driving under the influence puts the life of the driver and everyone else on the road at risk; (b)

answer; i believe its called ; checks   and balances;