The experimental (aka empirical) probability for your friend is 1/500 = 0.002 since she hit the bulls eye once out of 500 tries. This is a 0.2% chance.
To calculate the theoretical probability, we have to determine the area of each circle:
A = smaller circle area = pi*r^2 = pi*(0.25)^2 = 0.0625pi
B = larger circle area = pi*r^2 = pi*6^2 = 36pi
Divide A and B to get the theoretical probability
A/B = (0.0625pi)/(36pi) = 1/576 = 0.0017 approximately
This is fairly close to the 1/500 = 0.002 your friend got, which in my opinion means that her result is expected. She does seem a bit more skilled than expected since she managed to hit the bulls eye in 76 fewer tries (576-500 = 76). However, I would stick to the "result is expected" answer, since problems like this tend to have variability.
