How to form tag questions with may/might?
Polar bears may / might die of starvation, may / might not they?
or
Polar bears may / might die of starvation, may / might they not?
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Polar bears may / might die of starvation, may / might not they?
or
Polar bears may / might die of starvation, may / might they not?
Not is placed at the end of a tag question, so the correct option would be the second.
Polar bears may / might die of starvation, may / might they not?
You can also contract the tag, in which case it would be:
Polar bears might die of starvation, mightn't they?