Is it possible to use may and might in the same sentence to describe a potential outcome?
While Sara may recognise the car, Paul might not.
They both indicate that something is possible, but something that may happen is more likely than something that might happen.
So you may go to a party if Matt Damon invites you, but you might go to a party if your least favorite cousin invites you.
As stated by @ Anonym, might is the past tense of may. So you have to use might when you are referring to the past.
For example, even if it's likely that you went to a party last night, I shouldn't say, “you may have gone to the party’; I would say, “you might have gone to the party.”