“Do you know whether that would be covered by my insurance?”
You're at the dentist's office. The dentist tells you that you are grinding your teeth at night, and suggests that you get a mouth guard to wear while you're sleeping. You're worried about how much it will cost, so you want to know if your insurance will pay for it. You ask this to the dentist.
Do you know whether that would be covered by my insurance?
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Use this phrase to ask someone a question when you're not even sure if they know the answer to it. When you're asking a question that the listener does know the answer to, you can ask like this:
Would that be covered by my insurance?
In the example above, the speaker isn't sure whether the dentist knows anything about his insurance plan.
Use "would" in questions when you're asking about something that's not sure to happen yet. In the example above, the speaker isn't sure whether he will get the mouth guard yet. So he asks "Do you know whether that would..."
If the speaker had already decided to get the mouth guard, whether his insurance will pay for it or not, he would ask:
Do you know whether that'll (that will) be covered by my insurance?
Things that an insurance policy will pay for are "covered" by that policy. For example, a car insurance policy will "cover" the damage to someone's car if you get in an accident with them.
You can use the word "cover" with the following words:
cover the cost of the repairs
cover the (medical) procedure
cover the damages (like in a car accident)