Some people believe that we are predestined to be believers.  That we were chosen or "Predestined" to believe from our beginning.  I don't.  Some people like John the Baptist, etc. may have been born with a special purpose and destination, but generally, God creates life and gives us free will.  I don't think there is a special class of people preordained to be Christians--which would mean that there is another special class of people preordained to go to hell. 

I believe because of giving us free will, there are some things God either has chosen not to do, won't do, or can't do.  He can't save you if you don't want to be saved.  He can't make you obey his laws, etc., etc. The list is long.

But, since God can do whatever He chooses, I believe he can make a choice "Not to Know" something.  If God allows a sperm and egg to connect and knows what that life will choose before He creates it, then God is choosing whether you are damned, or you aren't--at the moment you are created.  That isn't a God quality.  He would be classifying people before they are conceived, or born!! 

He offered Jesus for everyone.  We choose.  I believe God hopes to the very end of your life that you will accept the sacrifice of his Son for your sin. And because he chooses not to know what you are going to do, He has hope for you.  Faith is the substance of things hoped for the evidence of things not seen.  I think God hopes.  "For God so loved the world that He gave his only begotten Son, that whosoever believes in Him might be saved."  Whosoever does not differentiate between chosen and not chosen.  Predestinated or not predestinated.  He has told us to spread the Gospel.  What's the point if you are doomed anyway.  Why tell us, "Go ye therefore and teach all nations..." if it doesn't make a difference. 

I think God has chosen to offer salvation to every person, and that God can make a choice not to know what they will do--so that he isn't creating pre--damned person.  

And no...I can't back what I think up with a distinct scripture.  I infer it from the Biblical descriptions of what the characteristics of God are.  All scripture.