Example of how natural selection occurs?

Lets say you have two bunnies. One has a long tail, the other has short tail. The one with the long tail died because a predator was able to catch onto the long tail and eat it. Therefore, the long tailed bunny can't pass on the characteristic of a long tail and that trait is no longer seen in bunnies. However, the bunny with the short tail isn't caught by predators as easily, and as a result, passes on the trait of a short tail to its offspring. After a long amount of time, no bunnies will have long tails because all the bunnies with long tails were killed out, and as a result, can't pass on the characteristic of a long tail. Bunnies then evolve to always have short tails.