negative question: already/yet

Doris: Hasn’t your sister finished her homework ____?
Emily: I don’t know.
(A) already (B) yet
Which choice is correct?

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Yet.
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Is there any milk in the fridge?
Is there some milk in the fridge?
Isn’t there any milk in the fridge?
Isn’t there some milk in the fridge?
The above sentences are quoted from Cambridge Grammar of English.
If “some” can be used in negative questions, why can’t we use “already” in negative questions?

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1-- Why do you think some (adj) and already (adverb) would have any functions in common?

2-- You can use ‘already’ but it is not the unmarked use, which is required for such a non-contextual sentence as the one given. What do you think is the difference between Is there any milk in the fridge? and Is there some milk in the fridge?
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Have you met John yet?/Is there any milk in the fridge?
Have you already met John?/Is there some milk in the fridge?

The first two questions are open–they just ask for information.
The last two questions suggest that the answer “yes” is expected.

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Yes, I agree.
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In what context can we use already in negative questions?

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Just as you said-- in a context where the answer “yes” is expected.
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  1. Hasn’t your sister finished her homework already?
  2. Has your sister finished her homework already?
    What’s the difference in meaning between the above two sentences? Both questions suggest that the answer “yes” is expected, don’t they?

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Nope. The first one is merely enquiring with impatience-- that’s the function of the negation.
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I am sorry to have made some typos. I have corrected them now.

This is my take:

Using ‘already’ with the negative here suggests that the speaker believes ‘finished her homework’ to be true, and is basically expecting confirmation of that fact.

The speaker might use this to contradict something that someone else expects or has said. For example:
Janie’s big brother: I’m going to go help Janie with her homework now.
Janie’s mom: Hasn’t your sister finished her homework already? I think she mentioned about an hour ago that she had managed to do it all herself.

This might be used to express surprise that ‘your sister’ might have already finished her homework. Something or someone has suggested to the speaker that ‘finished her homework’ might be true, and the speaker finds this surprising or hard to believe.
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  1. Is there some milk in the refrigerator?
  2. Isn’t there some milk in the refrigerator?
    What’s the difference in meaning between the above two sentences?
  1. Genuine inquiry. You don’t know whether or not there is milk.
  2. You are just about certain there IS milk. Perhaps you’ve just been told there is no milk. You’re annoyed. “Are you sure? Isn’t there some milk in the fridge?” Or you have your head in the refrigerator, looking about. You don’t see any, but you’re sure it should be there somewhere.
  1. Is there some milk in the refrigerator?
  2. Isn’t there some milk in the refrigerator?

If #1 is genuine inquiry, how about the following sentence?
3. Is there any milk in the refrigerator?
4. Isn’t there any milk in the refrigerator?
Isn’t #3 also a genuine inquiry?
What’s the difference between #1 and #3?
What about #4? Is #4 a genuine inquiry?