The Fermi Paradox seeks to answer the question of where the aliens are.
The Fermi paradox, named after Italian-American physicist Enrico Fermi, is the apparent contradiction between the lack of evidence for extraterrestrial life and various high estimates for their probability.
As many stars as there are in our galaxy (100 – 400 billion), there are roughly an equal number of galaxies in the observable universe—so for every star in the colossal Milky Way, there’s a whole galaxy out there. All together, that comes out to the typically quoted range of between 1022 and 1024 total stars, which means that for every grain of sand on every beach on Earth, there are 10,000 stars out there.
There isn't a proper nimber for the percentage of sun-like stars. But going with the most conservative side of that (5%), and the lower end for the number of total stars (1022), gives us 500 quintillion, or 500 billion billion sun-like stars.
Even the Milky Way has billions of these sun-like stars.
With high probability, some of these stars have Earth-like planets in a circumstellar habitable zone. In astronomy and astrobiology, the circumstellar habitable zone (CHZ), or simply the habitable zone, is the range of orbits around a star within which a planetary surface can support liquid water given sufficient atmospheric pressure. Many of these stars, and hence their planets, are much older than the Sun.
If the Earth is typical, some may have developed intelligent life long ago. Some of these civilizations may have developed interstellar travel, a step humans are investigating now. Even at the slow pace of currently envisioned interstellar travel, the Milky Way galaxy could be completely traversed in a few million years.
And since many of the stars similar to the Sun are billions of years older, Earth should have already been visited by extraterrestrial civilizations, or at least their probes. However, there is no convincing evidence that this has happened.
Conclusion
Even if the probabilty of lime is very small. There is enough sample space in the Universe that it is possible. This means that we are not alone in this huge Universe.
Reference:
Credits:
By Department of Energy. Office of Public Affairs - This media is available in the holdings of the National Archives and Records Administration, cataloged under the National Archives Identifier (NAID) 558578., Public Domain, https://commons.wikimedia.org/w/index.php?curid=156854
By ESA/Hubble, CC BY 4.0, https://commons.wikimedia.org/w/index.php?curid=8788068
By NASA/SDO (AIA) - http://sdo.gsfc.nasa.gov/assets/img/browse/2010/08/19/20100819_003221_4096_0304.jpg, Public Domain, https://commons.wikimedia.org/w/index.php?curid=11348381
By Chester Harman - Send to me personally upon request, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=64107813
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