The math in this thread is broken.
Just because there are 2 outcomes (gun player or not gun) does not mean there is a 50% chance. It's like saying there's two outcomes - you winning a billion dollars tomorrow or not winning a billion dollars. It isn't 50/50.
Regardless, if we assume the it is a 50/50 shot (which it isn't), then the example of the coin flip IS correct because the discussion is regarding taking TWO PICKS.
If you have one pick, then, in this scenario, it would be a 50% chance of a gun.
But if you have two picks, there's two 50% chances in isolation, however probability compounds. There are 4 outcomes from 2 picks:
Gun + Gun
Gun + Not Gun
Not Gun + Gun
Not Gun + Not Gin
There's a 1/4 chance of 2 guns
1/4 chance of 2 not guns
2/4 (or 1/2) chance of 1 gun
Therefore, there's a combined 3/4 chance, or 75%, that there will be an outcome of AT LEAST one gun.
But, as I said at the start, this is nonsensical as this isn't a 50/50 scenario. Again, if it were, then the above is indisputably correct.
Can we move on?