JohnKSa comments about a 2 MOA rifle and ammo fired by someone who can hold 1 MOA and the group size he'll shoot:
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It's more complicated than a simple addition of group sizes. It won't be a 3MOA group, but it will be between 2 and 3MOA.
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It is exactly a simple addition of shooter and bullet error on target. And if many groups were shot, they would be no bigger than 3 MOA but the smallest ones could be as small as 1/4th MOA. The rifle often shoots groups well under 2 MOA, the biggest group the rifle and ammo will shoot.
If the shooter fires a shot holding 1/2 MOA off his desired point of aim and the rifle shoots a bullet 1 MOA out the same direction, they will add directly. The bullet will strike 1-1/2 MOA away from the desired impact point. Reverse the directions for both and the error by the same amount and the bullet will go 1-1/2 MOA the other way; 180 degrees away from the first one. The two bullet holes will be a 3 MOA 2-shot group.
However, if many groups are shot in these conditions, it's possible that they could be somewhere between 1/8 and 3 MOA. The smallest ones are the result of compensation when the shooter's error is the opposite from the desired impact point from where the bullet's error puts it. Groups so shot are the records in competition.
I've shot two-inch 5-shot groups at 600 yards (1/3 MOA) and 1000 yards (2/10ths MOA) with aperture sights slung up in prone with .308 Win. I don't hold better than 3/4 MOA in prone and try to get shots off inside 1/2 MOA. But I don't claim the rifle and its ammo is a 1/3 MOA performer at 600 yards and a 2/10ths MOA perfomer at 1000.