The odds of that length of delay are pretty low. Common delays are less than 3 hours most of the time.

But I advise against seaparate tickets, especially on seaparate carriers. If there IS a delay of that length, the first carrier is not responsible for getting you to your final destination, but only to the connection airport. You will not be accommodated. Also, your bags, if you check them, may not make it all the way.