Mathematics · Probability

A disc has identical patterns on both its front and rear views. It possesses 3 axes of symmetry (1-1, 2-2, and 3-3) arranged uniformly such that rotating or flipping about axis 1-1 results in a horizontal reflection where the pattern changes orientation. Specifically, flipping about axis 1-1 changes the view, while flipping about axis 2-2 or 3-3 retains the exact identical view. If the disc is flipped once with respect to any one of these three fixed axes chosen uniformly at random, what is the probability that the disc DOES NOT retain the same view after the flipping operation?