Study this example situation:

You are looking for Ben. 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)

• It may be true. or It might be true. (= perhaps it is true)
• She might know. or She may know.

• It may not be true. (= perhaps it isn't true)
• She might not work here any more. (= perhaps she doesn't work here)

• A: I wonder why Kate didn't answer her phone.
  B: She may have been asleep. (= perhaps she was asleep)
• A: I can't find my phone anywhere.
  B: You might have left it at work. (= perhaps you left it at work)
• A: Why wasn't Amy 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)

• It's a strange story, but it could be true. (= it is possible that it's true)
• You could have left your phone at work. (= it's possible that you left it there)

• Sarah couldn't have got my message. Otherwise she would have replied. (= it is not possible that she got my message)
• I wonder why Sarah hasn't replied to my message. I suppose she might not have got it. (= it's possible that she didn't get it - so perhaps she did, perhaps she didn't)