The so-called problem of evil is a big issue in the world. According to the description, this problem exists because, given a good and all powerful God, evil should not exist.
Coming from a Calvinist perspective however, this problem is a non-issue. It is precisely because God is good that evil does in fact exist in this world, for we are evil.
Many people lament the fact of evil, and scream at God as to why evil must exist in this world. Strangely, I have never met anyone who wonders why there is still so much good in this world. Why is it that for example there are only 2 murders per month as compared to 2 murders per week? Why only one tsunami in 2004 instead of tsunamis every other month? Do people thank God for the fact that they have food on the table the next day, and that they were not struck by lightning today?
The fact of the matter is that none of us deserve anything good from God. Our wickedness caused the entire creation to be cursed (Gen. 3:17; Rom. 8:19-21), thus giving us natural disasters, and all wickedness in this world is caused by us. Upon what basis can wicked rebels expect God to continue to give them good things? We are not only wicked but ungrateful. When was the last time you, anyone, thanked God for the good things He has given to you this day?
The wages of sin is death (Rom. 6:23a). All of us sinners deserve death even while we live. God who is good must hate that which is evil and we are evil, so why should we rebel sinners think that the existence of evil is a problem for God? We deserve the evil fruit of our wickedness and should we blame God for our own wickedness? So is God supposed to restrain wickedness in this world and stop the murderers, rapists and thieves? Weren't you the ones who shout the most loudly about "free will" and how God cannot "force" anyone to do anything? Then when God leave us to our wicked "free will" designs, we ungrateful wretches complain!
Evil is not a problem for God; it is a problem for us. The presence of evil shouts how sinful and depraved we are. The attribution of the problem of evil to God is one more evidence of our wickedness before God.
So why does evil exist? It exists because of us. We are the problem, not God. The problem is not "How can God exists if there is evil in this world?"; it is "How can good exists if we humans are in this world?".