Instead of net coding them as individual shots, just multiply the hit chance by 3 as it's essentially the same thing. Client wise, it's different but mathematically it's the same probability of hitting.
If you had X chance of doing it of Y amount of shots. ((100-X / 100) ^ Y). This would work out the same probability as (X * Y).
5% chance of hitting over 3 shots. ((95/100)^3) = 0.857. That's a 85.7% chance of NOT hitting. 100% - (5% * 3) = 85%.
Using the equation given above, you can get the true chance of hitting which would be 14.3% of hitting a 5% shot at least once over 3 shots, the former of 14.3% provides a precise probability but the later would provide a nicer roundup for the players.