Well, maybe not so much the Universe, as our own galaxy....
I recently came across a statement that there was an estimated 100 billion stars in our galaxy. I started to wonder, about the odds of us encountering sentient life in the galaxy, so I started running some rough calculations, just to estimate.
Astronomers estimate that approximately three out of four stars may harbor planets. (Basically, any unary system, plus any binary system where the companions orbit at least as far from one another as Pluto orbits our own star.) Again, these are rough estimates. So, maybe 75 billion planetary systems exist in our own galaxy!
For the moment, lets call the probability of a planetary system harboring a planet capable of supporting life is p. Lets call the probability of life developing on such a planet l. Lets call the probably of sentient life developing from more primitive forms (at any point, without regard to the time it takes) s. Further, lets assume that the average age of all stars in our galaxy is close to 5 billion years. And, lets assume that the time it takes for sentient (not necessarily civilized!) life to develop is close to what it took here on Earth, and that a sentient life form remains on the planet for about 100,000 years. (This is similar to the span of time that has been postulated since the first cavemen appeared here on earth.)
Then, we can guess that the number of planets which currently harbor sentient life in our galaxy to be expressed by:
75 * 10^9 * p * l * s * 100,000 / (5 * 10^9)
1.5 * 10^6 * p * l * s
As probabilities p, l and s approach unity, we have approximately 1.5 million sentient species in the galaxy right now! (Regardless of whether they are space-faring or not.) This also ignores galaxies other than our own (there may be 100 billion such galaxies!)
Assume 1 per cent for each of these probabilities, and an entirely different picture comes up:
1.5 * .01 * .01 * .01 = 1.5 species in our galaxy right now.
The real question is, what are the values of p, l and s. Well, lets look at them:
Looking at our own Solar system, we have 8, 9, or more planets, and a number of moons. At least one of them supports life (Earth!) Its likely that at some point in its history, the conditions for supporting life were present on Mars, and it is also possible that conditions for supporting life may exist elsewhere just in our own system. (We are considering various moons, for example.) So it does not seem unrealistic to hypothesize a fairly large value for p. Let's randomly pick a value of .75.
The probability of l still seems a bit unclear. I certainly hope that we find it to be fairly large, but observationally we have not got any information other than our own planet. A sample size of 1 is too small to tell us anything. But, if we assume that other places in the galaxy are somewhat likely to have undergone similar processes as our planet did, the probably may be at least .25. (Again, a semi random value.)
With those values, we should have 1.5 million * .75 * .25 = 281,250 planets harboring life (of any kind) in our galaxy.
What is the value of s? Well, that's the biggest question. But even if it is quite small, say .01, then we still have a nice value of around 2000 different sentient species in our galaxy right now!
I'm really hopeful that now that we are getting the instrumentation to locate these extra solar planets, and even tell some things about them, such as their chemical makeups, etc. that we may be able to start finding evidence of these ... I hope that in the coming decade or two we will start sending out the first extra-solar probes to start are more direct observation of some of the other planetary systems. (We know that it costs quite a bit to build such a probe. But what is the incremental cost for additional probes? Could we send out 100, 1000, or even 10000 such probes to different systems?