1. Universe is 13.82 BY old.
While the universe is 13.xx billion years old, you can cut the first couple bn years, as there weren´t enough heavy elements (i.e. anything above H and He) to support rocky planet as those (the elements, not the planets
) were generated via supernova explosions as the universe aged (not that this changes a whole lot, mind you).
The main problem with finding other intelligent life in the universe is twofold, as I understand it.
One: The universe is bloody big. Even if there would be thousands of advanced species out there right now, the distances between two of them (assuming somewhat even distribution) would be what, one species per several hundred thousand galaxies.
Two: Even if a thousand advanced species would evolve in a single galaxy, the timespans involved are mindbogglingly large.
Say, we start counting from Big Bang +5 billion years as the time when enough heavy elements were there to support life.
Lets also assume it takes another 3 bn years for life to evolve from simple singular cells to something intelligent.
This leaves us with more than 5.5 billion years over which those 1000 species are spread out. The chances that two of those achieve the level of radio use/space flight at the same time are incredibly low.
Arthur C. Clark called this: Your space explorers will find "Angels or Apes" but no men
Why? Consider the history of Planet Earth. Let the height of the Empire State building represent the 5 billion year life of Terra. The height of a one-foot ruler perched on top would represent the million years of Man's existence. The thickness of a dime will represent the ten thousand years of Man's civilization. And the thickness of a postage stamp will represent the 300 years of Man's technological civilization. An unknown portion above represents "pre-Singularity Man", the period up to the point where mankind hits the Singularity/evolves into a higher form/turns into angels. Say another dime. Above that would be another Empire State building, representing the latter 5 billion years of Terra's lifespan.
If you picked a millimeter of this tower at random, what would you most likely hit? One of the Empire State buildings, of course. So, assuming only one civilization develops on a planet, chances are the first-in-scout starship Daniel Boone will discover mostly planets that are currently empty of alien civilizations (but they might have an almost 50% chance to discover valuable Forerunner artifacts or other paleotechnology).
If you only use the section with an alien civilization, you have a ruler and two dimes worth of apes and angels, and a postage stamp worth of near Human civilization. Ergo: apes or angels, but not men.