You can use may in both sentences. In fact, I think using 'might' in the first sentence is wrong, or at least archaic (so old-fashioned that people would laugh). May is definitely better when you are talking about permission ("You may leave when you have finished your chores"). In the case of the patient, I would use 'may' here too, especially if I'm talking to the patient or someone who cares about them. 'Might' sounds a bit flippant, like you have no control, you don't know the probability, and it's not that important. 'May' sounds a bit more hopeful.