If God is sovereign, why pray for the lost?

From time to time I get questions on a theological topic or some other matter related to the Christian life and I thought I would use this part of the site to share some of these.

A few days ago I received the following question by e-mail:

I've been trying to understand Reformed Theology.  R. C. Sproul is one of my favorite teachers.  I have alot of his tapes and videos.  My main problem is:
Praying for the salvation of a person, how does one approach God?  This might sound strange, but if we are chosen, which I believe, from the foundation of the world, then how do I ask God who does not change His mind to save someone that might not be chosen.  Can you feel my dilema?  I might not be explaining it quite right.  I know that we don't know who is chosen and who is not.
Do I just keep praying and asking, like the story goes?

My answer follows: