The Question of Original Sin

Are humans born sweet and innocent, but learn how to be sinful or are we born with a sinful nature? This is how I phrase the question of Original Sin. I heard an illustration that makes it rather clear, I think.
Once upon a time there was an old woman who owned a farm. On this farm she had a chicken coup. Surrounding this farm was a wooded area that was inhabited by weasels. The weasels liked to eat the chickens. So the old woman would set traps for the weasels. When she caught one, she would get her hoe that was filed down to a sharp point and kill the weasel.
One day she happened upon a nest of baby weasels. She did not say, “Oh what cute little weasels, they have never done anything wrong. They are so sweet and innocent. I will just let them be.” She said to her helper, “Go and get my sharpened hoe and I will stay here and make sure the babies do not get away.”
The point is that a weasel is going to be a weasel and humans are going to be humans. Unless we change from the inside out by the power of the Holy Spirit and put on a different nature (the nature of God by faith in Jesus Christ) then we will suffer the same fate as the baby weasels.