How do you define personal responsibility? When something bad happens that involves you, how do you know whether or not you bear some responsibility for it?

I would define personal responsibility by taking responsibility for one's actions. For example, turning in homework assignments, or keeping a promise and ones word. Responsibility is a particular trouble of obligation upon one who is responsible, also trustworthiness or loyalty. 

When something bad happens that involves me, I take responsibility either way. For example, There was a time I gave my brother permission to go to the park without my parents consent. The responsibility fell on me because, I didn't ask permission for him, nor did I watch him. So when something bad happens that involves me I am required to take responsibility.