the chances of a random address collision are very very slim. search for it.
personally i generate my paper wallets using bitaddress.org on an offline computer booted from a linux live CD but that's just how it was done in 2012. so much easier now, haha.
How can you access bitaddress.org on an offline computer? And doesn't bitaddress.org owner then know your private key?
i boot tails and access the site, then disable internet connection. then generate new addresses, print and turn off the computer. bitaddress.org does everything in your browser no info given to the site. it is open source so you can be confident others have reviewed the code.