Yeah, that is a tough one. There are several open discussions regarding their use in present versus past tense. So, as Leo wrote, probably the most correct way is to use "may" is for permission and "might" for possibility. But it's also common to use "may" for something that is more likely to happen than if you were to say that it "might" happen.

Hi there. It always is a pretty tricky question to explain the difference between the modals 'may' and 'might'. Basically, the endeavour is more of an art rather than an actual science. Strictly speaking, the use of the preterit with modals put the emphasis on the fact that the speaker is further removed from the action than if he had used the regular one. However, in the case of 'may' and 'might', it might not be as straightforward, and the usages vary between American and British English. 'It might rain this morning' indicates a possibility. You have seen the weather forecast, the sky is cloudy, or you live in England (in which case 90% of your days are rainy), so you've got some evidence that it's going to be raining. 'It may rain this morning'... It doesn't really sound right. Nowaday, 'may' has been restricted to individualised usages, and even so, it's not all that common outside of the UK. For instance, you might say 'You may use this computer' as to give the indirect permission to someone to use a computer, which would be pretty close to 'You can use this computer'. Anyway, it's a pretty tough question. Generally speaking, if you're in doubt, going for 'might' is more often the right-sounding one. Hope that helped.