Question about evolution?

Every mutation is random. If a mutation is bad for reproducing and/or living, then the mutated species will not survive long compared to another mutated species that comes from the same origin. Therefore the only ones that remain are the ones that can survive long, despite the randomness of it all. A good example is that of a type of butterfly, I don't remember where. It stayed a lot around a black type of birch, but was white. Because of pollution in the area, some got genes that made them black. Those black butterflies had a natural camouflage against predators because of the color of the trees. The white type nearly disapeared since they were the only ones their predators could easily see, while the black type remained numerous. Because of a random genetic mutation, the species got a better camouflage.