Example 1. 1. He may not have heard you.
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Example 1."May" and "might" are used here as modals for conjecture. "May"(#1) is a bit stronger in the certainty of the conjecture.
1. He may not have heard you. Call him again.
2. He might not have heard you. Call him again.
Example 2."May" and "might" are used here as
1. You may not borrow my car.
2. *You might not borrow my car.