Short version - if something has a 1% chance of dropping...

It's not unreasonable to expect that you'll see at least one if you kill the boss a hundred times. (It's 63.4% reasonable, if you care.)

It isn't guaranteed to drop if you kill the boss a hundred times.

In fact, it isn't guaranteed to drop ever.

If you've killed the boss once, ten times or a million times, the chance for the thing to drop on your next kill is still 1%.

You can do some math stuff and generate a bell curve showing how many runs a big group of people would require to each get their mount.

That curve doesn't say anything about how long YOU will take to get your mount.

If you get your mount after a certain number of tries, or have failed to get it a certain number of times, the curve can give you an idea whether you've had 'bad luck' or 'good luck' compared to Joe Average. 'Bad luck' and 'good luck' are vague terms but can be interesting to talk and bitch about even if they aren't all that useful.
...I think that's about it. Most D&D players have thought this through but it might be new for some folks.
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Everything in war is very simple. But in war, even the simplest thing is difficult.