I was on an organized day tour a couple of years ago. Several miles into the ride, I felt my tire get kind of lumpy.
Quick inspection revealed a growing bulge. I took the tire off to see what was going on and found that the tire was worn paper thin, but the cording was not yet showing. I lined the inside of the tire with a tire patch, but knew it would not last long.
No spares tires were available, so I proceeded with the ride. Just when I passed two old ladies out for a walk, KA BAAAM! the tire exploded. The tube poked through the tire, wore thin and then exploded. It was an enormous sound - very much like a big caliber gun shot. The old ladies almost jumped out of their skin. It shocked me too!
I THINK that you can at least try to inspect your tires once in awhile by taking the tire off and feeling both sides of the tire between your thumb and forefinger. It is worth a try, anyway.