1. You would rather not drive this afternoon.

2. You had better not drive this afternoon.

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Which expression is right? are both right? Then what is the difference between them?
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3. You would rather stay at home than go out.

4. You had better stay at home than go out.
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Is Sentence 4 right? Is only #3 correct?

Both are right, but they mean different things.

1 and 3 mean "you" have a choice.

2 and 4 mean that "you" are being warned not to do something.