May and might
We use the modal verbs
- I'm not sure I'll go to the party. I may be away.
- Don't drop by at 7:20 PM. I might be watching TV.
- Please, prepare something to eat. Mr. Johnson might be hungry.
- We may not be able to go to school this week.
There isn't much difference between the two. So you can say:
- "John might be at home" or "John may be at home".
- "I may visit Mary" or "I might visit Mary".
Sentences formed with
- I may be away at 10 PM. (35% likelihood)
- I might be away at 10 PM. (20% likelihood)
However, when the situation is unreal, only
- If I were a bit smarter, I might go to college. (The speaker won't become smarter, so the situation is unreal)
If you want to emphasize progression of a situation, you may use the continuous form of the verb after the modal.
- Don't drop by at 7:20 PM. I may/might be watching TV.
If you're using the reported speech,
- "I may be late," said Frank. In reported speech: Frank said that he might be late.
Read about Modals in the Reported Speech.