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?

There's really not a right way to answer this question. Honestly, you know that you have to take personal responsibility because you'll notice it. You'll notice that "Hey. You know. This thing really involved me and it's my job to take responsibility for it." Personal Responsibility is something that you stand up for if you think/know that you have to.

Personal responsibility is knowing what you are responsible for. Like whether you feel responsible for your own learning or not. If something bad happens to you, you will know if you are responsible for it if there is something you did, and you regret it. However, it may not always be a bad thing. Sometimes we do something good, and still regret it, and the result is something bad happening.