Praying The Rosary For World Peace?

I saw a car on the road this morning with a bumper sticker that went something like this: "Pray the rosary for world peace". Obviously, the driver was Catholic. Assuming that they are a real Catholic, and not just one of those nominal types who likes the pretty candles, but ignores all of the icky stuff about sin and sacrifice, their Catholicism says certain things about their worldview. Specifically, it means they believe in original sin, the idea that humankind is in a fallen and rebellious state and is irredeemable without Christ. They also, one would assume, believe that wars, genocides, etc. are a result of this sinful state. Lastly, while this one is a little more complicated than it sounds when simply stating it, Catholics believe in free will.

So, if one believes in a world where fallen and sinful men are free to exercise their will, isn't praying for world peace a little like praying for a winning lottery ticket when you don't ever play the lottery? It's a beautiful idea, but one that seems unlikely to occur anytime soon. With God all things are possible, but might not a better use of our finite prayer time be intercession on behalf of more likely causes? Should we pray for things that seem to go against God's permissive will? Is it enough to pray for a beautiful idea simply because it is a beautiful idea?