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May is used to express what is possible, factual, or could be factual. For example,

We may go on vacation.

I may have dessert after dinner.

He may lose his job.

Might is used to express what is hypothetical, counterfactual, or remotely possible. For example,

If you hurry, you might get there on time.

If I had shown up on time, I might have kept my job.

If I win the lottery, I might buy a Ferrari.