As for you, you meant evil against me, but God meant it for good, to bring it about that many [or numerous] people should be kept alive, as they are today. [Gen. 50:20]
A familiar and very beautiful verse, how comforting it is to know that God works all things for good. But note, this verse isn’t simply saying that God brings good out of evil situations, and it isn’t saying that God turns around evil situations to be good situations. The implications of such approaches is God slipped up letting the evil thing happen in the first place and had to use what was available to him, namely the evil event, to re-create good; and, it also diminishes the evil; I.e. ‘don’t worry about the evil, because I will make it good and it will all be ok.’
However, what is going on here is two accomplished intentions of the same event. What Joseph’s brothers meant for evil, namely selling Joseph to slavery out of Jealousy, - this very same event, was intended to happen by God for good, and inevitably a good purpose.
So the paradox between God’s sovereignty and man’s responsibility is scripturally compatible in this passage. God intends and ordains this event totally to bring about good, and was in no way the author of its evil. Man, however, authored the event in its evil to bring about evil – and as such is responsible. So God can be totally sovereign over an event and ordain it to bring about its good, yet man authors the evil within it (and within God’s sovereignty) for evil intensions.