Теория:

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.
 
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2. If we are referring to possibility, 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 head office.
 
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Certain and uncertain answers to questions.
 
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.
 
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4. We also answer Wh-questions with ‘certainty’ or ‘uncertainty’.
 
What is his name?- It’s Brown. It may/might be Smith.
Источники:
theodysseyonline.com
www.oscoconstructiongroup.com
www.designtrends.com
L.G. Alexander. Longman English grammar practice for intermediate students- Harlow: Longman, 296p.