Problem of Evil: "Difficulty posed by the existence of evil (both moral evil and natural evil) in a world created by a God who is both completely good and all-powerful. Some atheists argue that if such a God existed, there would be no evil, since God would both want to eliminate evil and would be able to do so. An argument that evil is logically incompatible with God's reality forms the logical or deductive form of the problem. An argument that evil makes God's existence unlikely or less likely is called the evidential or probabilistic form of the problem. Responses to the problem include theodicies, which attempt to explain why God allows evil, usually by specifying some greater good that evil makes possible, and defenses, which argue that it is reasonable to believe that God is justified in allowing evil, even if we do not know what his reasons are."
Evans, C. (2002) Pocket Dictionary of Apologetics & Philosophy of Religion. Downers Grove, IL: InterVarsity Press.