May / might

We can use 'may' to ask for permission. However this is rather formal and not used very often in modern spoken English

May I go to the concert? (This means the same as "Am I allowed to go to the concert?") As a result, using may could create some ambiguity. For example: I may go to the concert. This is ambiguous. Does it mean "I am allowed to go to the concert" or does it mean "I might go to the concert"? When you have a situation like this, use might (or a version of allow) to eliminate the ambiguity. For example: I might go to the concert. I am allowed to go to the concert.

might

We use 'might' to suggest a small possibility of something. Often we read that 'might' suggests a smaller possibility that 'may', there is in fact little difference and 'might is more usual than 'may' in spoken English.

She might be at home by now but it's not sure at all. It might rain this afternoon. I might not have time to go to the shops for you. I might not go.

For the past, we use 'might have :

He might have tried to call while I was out. I might have dropped it in the street.