the size of the universe and the likelihood of intelligence

I recently came across an interesting quote in an article I was reading:

If the universe lasts forever, then any event that can happen, will happen, no matter how unlikely. In fact, this event will happen an infinite number of times.

The article has to do with the laws of physics and why time must eventually end, but I had thought about this idea previously while thinking about abiogenesis and the evolution of intelligence.

The large scale structure of the universe seems uniform. Once you pull out far enough, it's all filaments and voids. Since it's basically the same everywhere, the likelihood of an event occurring in one part of the universe should be the same as the likelihood of it occurring in another part of the universe.

Of course this depends on the type of event and scale we're talking about. Supernovae are a relatively frequent occurrence at the level of individual galaxies. But there might be 100 gamma ray bursts per day across the entire universe (which is considerably larger).

We could generalize this and say that for any cosmological event there's a particular probability density (P) for it which could be expressed as the likelihood of finding such an event occurring in a randomly chosen galaxy the size of our own. For the above two examples, P_supernova > P_{gamma-ray-burster}, though we don't know by exactly how much.

So what's the P for life? If you chose a Milky Way-like galaxy in the universe at random, how many planets could you expect to find in it, on average, that had ongoing processes of biological evolution taking place?

What's the P for intelligent life? What's the scale of the universe at which P_{intelligent-life} = 1? What's the average density of intelligent life for the universe as a whole? (Since the universe is roughly uniform in condition, it makes sense that everything is about equally distributed.)

As I mentioned in the previous post, if the Medea hypothesis is true, it might be very difficult for life to evolve even to the level of complexity and order we see in Cambrian biology, let alone intelligent life like our own. The scale of the universe at which P_{intelligent-life} = 1 might be extremely large, maybe even larger than the observable universe. It would explain why we don't see any intelligent civilizations even though we should if any existed.

It also might explain why the universe is so large. According to some cosmologists, the difference between the size of the observable universe and the actual universe is the same as the difference between an atom and the surface of the earth. (Mind you, the observable universe is already unfathomably large.)

Why do we observe such a large universe? Perhaps it's because that's the only kind of universe that can support the sort of life that would evolve to ask the question, "Why do we observe such a large universe?" Smaller universes might exist, though they never reach a scale large enough for intelligent life to become probable.