Study the information about modal verbs.
Expressing certainty and possibility.
1. If we are certain of our acts, we use be or any full verb.

Jim is at home. Jim works at home.
2. If we want to express that something is possible, we use may, might, could + be/have been.

Jane may/might/could be at home now.
Or we use may, might, could + full verb
Kate may/might/could work at the head office.
1. A ‘certain’ question may produce an ‘uncertain’ answer.

Does she like apples?- She might (do). She may (do). She could (do). She may not.

2. An ‘uncertain’ question may produce a ‘certain’ answer.

3. We use do/done to replace other verbs, though this is optional.
Will you catch the early train?- I may/I may do.
4. We also answer Wh-questions with ‘certainty’ or ‘uncertainty’.
What is his name?- It’s Brown. It may/might be Smith.
L.G. Alexander. Longman English grammar practice for intermediate students- Harlow: Longman, 296p.