Don't be confused. "Might" is the past form of "may". "I may come with you," said John. = John said he might come with us. (reported speech: everything is dropped into the past) When you use it to express a possibility, "may" indicates a likely possibility, whereas "might" means the chance is less likely. You can do this with all the modal pairs. It may rain tomorrow = there's a good chance, I think. It might rain tomorrow = I could be wrong; but there's a slim possibility.

-MAY for FORMAL PERMISSION - ' May ' is rather formal and not used often in spoken english, but it is used to ask formal permission . - May I go out? - May I borrow your book? -------------------------------------------------------------------------------- TO EXPRESS POSSIBILITY When you want to express something is possible you can use 'May' or 'Might' .Usually "might" suggests a smaller possibility that "may" . Also "might " is more usual in spoken english. -It may rain later ( possibility) -It might rain this week-end ( less possibility) -You might not go to the ceremony !

There is often little difference in meaning, but might suggests that there is less possibility.

I think that you can use 'may' and 'might' interchangeably. Both mean the supposition.