Study this example situation:
You are looking for Bob. Nobody is sure where he is, but you get some suggestions.
He may be in his office. (= perhaps he is in his office)
He might be having lunch. (= perhaps he is having lunch)
Ask Ann. She might know. (= perhaps she knows)
We use may or might to say that something is a possibility. Usually, you can use may or might, so you can say:
It may be true. or It might be true. (= perhaps it is true)
She might know. or She may know.
The negative forms are many not and might not:
It may not be true. (= perhaps it isn’t true)
She might not work here anymore. (= perhaps she doesn’t work here)
Study she structure:
I / you / he (etc.) | may, might | (not) | be (true / in his office, etc.)
I / you / he (etc.) | may, might | (not) | be (doing / working / having, etc.)
I / you / he (etc.) | may, might | (not) | do / know / work / want, etc/
For the past we use may have done or might have done:
A : I wonder why Kate didn’t answer the phone.
B : She may have been asleep. (= perhaps she was asleep)
A : I can’t find my bag anywhere.
B : You might have left it in the store. (= perhaps you left it in the store)
A : I was surprised that Sarah wasn’t at the meeting yesterday.
B : She might not have known about it. (= perhaps she didn’t know)
A : I wonder why David was in such a bad mood yesterday.
B : He may not have been feeling well. (= perhaps he wasn’t feeling well)
Study the structure:
I / you / he (etc.) | may, might | (not) have | been (asleep / at home, etc.)
I / you / he (etc.) | may, might | (not) have | been (doing / working / feeling, etc.)
I / you / he (etc.) | may, might | (not) have | known / had / wanted / left, etc.
Could is similar to may and might:
It’s a strange story, but it could be true. (= it may / might be true)
You could have left your bag in the store. (= you may / might have left it there)
But couldn’t (negative) is different from may not and might not. Compare:
Sarah couldn’t have gotten my message. Otherwise she would have called me. (= it is not possible that she got my message)
I wonder why Sarah hasn’t called me. I suppose she might not have gotten my message. (= perhaps she didn’t get it, and perhaps she did)