May/ Might is used to ask question, take permission or make requests. Likewise we use ‘may / might‘ to answer questions.
May I come in? Permission
May I leave early? Permission
May I use your phone? Permission / Request
May I have a glass of water? Request
May I sit her? It is too hot near the window. Permission / Request
May I know your name, please? Question
May I know why you were absent yesterday? Question
You may leave early.
Yes, you may.
No, you may not.
Might I borrow your pen for a minute? Permission / Request
The word ‘might’ is more polite and informal.