The more scientific approach uses variants of the Drake Equation. I'll use the variant from the recent paper A New Empirical Constraint on the Prevalence of Technological Species in the Universe by Frank and Sullivan.
We define the ‘‘A-form’’ of the Drake equation, which describes the total number of technological species that have ever evolved anywhere in the currently observable Universe:
A = Nfpnpflfift
where N is the total number of stars, fp is the fraction of those stars that form planets, np is the average number of planets in the habitable zone of a star with planets, fl is theI first encountered the Drake equation in high school from Carl Sagan's book Cosmos. The conclusion that there must be life out there from the equation never satisfied me because of our inability to measure the f values.
probability that a habitable zone planet develops life, fi is the probability that a planet with life develops intelligence, and ft is the probability that a planet with intelligent life develops technology (of the ‘‘energy intensive’’ kind such as that of our own civilization).
Frank and Sullivan's computations show that we expect there to only be life on Earth, say A=0.01 then f = flfift must be at most 2.5 x 10-24.
Seems small but is it really? 2.5 x 10-24 is roughly the probability of flipping 78 coin tosses and having them all come up heads. Maybe life requires 78 50/50 independent events to occur. Or 1060 independent events each with 95% probability. 1060 doesn't seem that big.
Our attempts at finding life, whether by SETI or Mars soil or UFOs have so far turned up nothing substantial. We just might be the only ones out there.
By no means am I arguing that we give up the search. I could be wrong, f could be much larger than 2.5 x 10-24. Let's keep looking, perhaps exploring the ice caps of Mars or the moons of Jupiter, keep listening the the stars, explore new ways to probe the galaxy. It would be incredible to find extraterrestrial life, but just don't be surprised if we don't.