The multiverse and improbable outcomes

I've been occupying my mind the last couple of weeks by going deep on a few ideas of a philosophical nature, mostly inspired by my recent reading of Neil Stephenson's Anathem. If you like books that make you think thoughts and also take you on wild sci-fi adventures, read Anathem. I'm sending the paperback on a tour of as many friends as I can get to read it and buying myself a hardcover copy that I can read a few more times and annotate. It's that good.

So here's a thought that's been bothering me about the multiverse theory. To summarize it very succinctly, the multiverse theory holds that, every time a random quantum-mechanical probability is resolved (for example, an unstable atom decays or does not), new universes are spawned to reflect each possible outcome. So in one universe an atom splits and in another it doesn't. With the incomprehensible number of quantum events taking place throughout the universe at any given moment, the number of universes that this idea would give rise to is vast on a scale beyond my ability to even attempt to convey it.

So here's the idea that's been sending my brain in circles: What if there is some very common quantum-mechanical effect that, for example, has a 90% chance to cause the entire universe to explode in fire during any given second. So after every second, there are nine universes in which everything has been annihilated and one in which it has not. Then after another second, that survivor universe has spawned another ten outcomes, nine of which are on fire. And so on and so on for trillions of years. What if ten copies of humanity are being spawned every second, and the version writing this post, and the version reading this post, are the fraction of a fraction of a fraction of a fraction, the tiny surviving remnant of a vast apocalypse?

This is basically the anthropic principle raised to the highest possible degree - what if the universe we inhabit at any given moment is, in fact, one of only a very tiny fraction that's managed to survive as long as it has, and the only reason that we perceive the universe as being a stable and constant phenomenon is that all the versions of the universe that have demonstrated its inherent instability resulted in all observers being instantly destroyed?