You probably should rephrase the question to how much precision do you need?
Thank goodness someone finally provided this clarification. This discussion had run to over 3 pages and yet, clearly no one had a clue what any one else was talking about because people were sometimes using the term "accuracy" instead of precision...
Error propagation relates to handling the errors which are reported as standard deviation for a given variable. Are you saying that the standard deviation of a "1/2 moa rifle" is 1/2 moa and the standard deviation for a "2 moa shooter" is 2 moa?
It takes more than 3, or even 5 or 10 shots to characterize the distribution and thereby provide the standard deviation of the distribution. The short answer is that no one is claiming that when someone calls a rifle an X MOA rifle that they are stating that the standard deviation/variance of the probability distribution function of the rifle's points of impact is equal to X MOA.
The math is a very good approximation of what will happen when two different systems with two different accuracy measurements of the general type under discussion are combined.
If the definition of a 2 moa shooter is someone who can hold the centerline of the bore within a 2 moa circle as the bullet exits the barrel, and they have a rifle capable of keeping all shots within a 1/2 moa circle centered about the centerline of the bore as the bullet exits the muzzle, the worst group should be 2.5 moa.
While that is correct, it is important to understand that getting that worst case group size in any group with a reasonable number of shots is very unlikely.
It would require that all of the following things happen within the number of shots fired for the group.
On one of the shots in the group, all of the following must be true:
1. The accuracy error of the rifle must be at or near maximum.
2. The accuracy error of the shooter must be at or near maximum.
3. The accuracy error DIRECTION of BOTH the rifle and the shooter must line up very closely for this shot.
That puts this shot on the extreme edge of the possible group size.
On another one of the shots in the group, all of the following must be true.
1. The accuracy error of the rifle must be at or near maximum.
2. The accuracy error of the shooter must be at or near maximum.
3. The accuracy error DIRECTION of BOTH the rifle and the shooter must line up very closely.
4. The accuracy error DIRECTION of both the rifle and shooter must be very nearly opposite of the accuracy error DIRECTION of the previously described shot.
That puts this shot on the extreme edge of the possible group size very nearly opposite the other shot described.
If ANY of the above 7 requirements are not met, the maximum group size will not occur. It takes all of them occurring within the number of shots in a group or the group size will be less than the maximum group size possible.
Stated another way what we need to occur is the following:
Each shot's error is composed of a Shooter error which has both magnitude (size of the error) and a direction (direction from the point of aim--up/down, up at a 45degree angle, etc.) and a Rifle error which also has both a magnitude and a direction.
Sm (shooter error magnitude) Sm1 would be the shooter error magnitude for shot 1.
Sd (shooter error direction)
Rm (rifle error magnitude)
Rd (rifle error direction)
Smax is the maximum error magnitude that the shooter can cause.
Rmax is the maximum error magnitude that the rifle can cause.
So what we need is for all of the following to be true for two of the shots in the group.
Sm1 = Smax
Sm2 = Smax
Rm1 = Rmax
Rm2 = Rmax
Sd1 = Rd1
Sd1 = Sd2+180degrees
Rd1 = Rd2+180degrees
If you think it's easy to get that many numbers to line up just right, you just might lose a lot of money on lottery tickets...