You have a provided an excellent example. Where I think it is a lot harder to comprehend the numbers working out on a completely random basis is in the origination of incredibly complex systems in species that did not have them resulting in an end state different from the one that provided the survival advantage along the way. So the feather mutation flourished because it provided warmth but that actually ended up leading to flight. And the numbers would seem more difficult with all the little bits and pieces that make up the eye but which until they come together to produce vision seem to have very little survival advantage.
The process is not quite as random as some people seem to think. The laws of physics put a very strong constraint on what is and is not possible. Vision is based on the fact that some chemicals absorb specific wavelengths of light. Even single-cell organisms have eyespots. Eyes have arisen many times, in many different forms.