What are some of the non-religious explanations for existence of evil in the world?

Actually the main problem with the existence of evil is for certain religions to explain it: How to make the existence of evil compatible with a benevolent God?Of course, there are several different explanations for this apparent contradiction. Anyway, for non-religious people, there is no such problem to solve. Evil (bad things happening) can be explained by random chance; evil people can be explained by the desire of individuals to survive and prosper, and more in general, by psychology.

Only in the case of believing in a religion, does the problem arise: How can God ALLOW such-and-such things to happen?