Both "might" and "may" have multiple meanings, and both are correct in those sentences. Most native speakers (myself included) would probably consider the two to mean basically the same thing. I looked up the difference and found these: https://www.wordnik.com/words/may https://www.wordnik.com/words/might Both words can be used to mean that something is possible. But the second definition for "might" says that "might" is weaker than "may." I would agree with that. If someone said "I might pass the exam" I would think they are less sure of passing the exam than if they said "I may pass the exam," but both sentences would convey a level of uncertainty. If there is a difference in meaning, it is not a big difference.

"might" is about possibility, while "may" is about permission: It might rain tomorrow. The local government says that bars may remain open until 2AM. In actual use, though, I often see "may" being used where "might" would be better.