In the following context:
You will be called within 1 to 2 hours
Does "within" imply between 1 and 2 hours? Or anytime from now, until 2 hours?
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The phrase means:
You may perhaps be called within an hour. You will definitely be called within two hours.
There is no implication that your being called within one hour is any more likely than your being called between one and two hours.
Or to put it more cynically: the sentence boils down to this.
If you are not called within an hour, you will be called within two.
Since the frame within two hours by itself includes within one hour, the explicit statement of the latter is superfluous. It's probably in there just to give you a false hope that the wait won't be as long as it is likely to be.
It's like when you're running late coming home for dinner and you call your spouse to say:
Sorry, babycakes, I got held up at the office. I'll be home in an hour, two hours tops.
That gives your spouse the feeling that you are going to try to be home by the earlier time (one hour) while still giving you the wiggle room to stop by your paramour's for a quickie en route, since what you've explicitly promised is just the later (two hours).
From a native speaker:
I may be in the minority here, but within 1 to 2 hours tells me between now and one hour, and at the most between now and two hours. Within does not refer to the range between the one and two hour mark, but to the period inside now and before one hour is over, and certainly before two hours is over.