Appeal to Probability
If I play the lottery long enough, I'm bound to win, and I can live on the prize comfortably for the rest of my life! Yes, it's possible that if you play the lottery, you'll win. Somebody has to. The logical fallacy here is to confuse the possibility of winning with the inevitability of winning. Of course, that doesn't follow.
In our study of cognitive bias (also available in compiled form here), we learned that numerous biases result from the misapplication or misunderstanding of probability in a given situation. Examples include the base rate effect, the gambler's fallacy, the hindsight bias, the ludic fallacy, and overall neglect of probability. Use the tag cloud to the right to learn more about each. We are, as a species, generally bad at estimating probability, especially when it affects us personally.
Various arguments about the Drake equation can fall into this trap. The Drake equation, developed by astrophysicist Frank Drake in 1961, provides a set of guidelines for estimating the number of potential alien civilizations that might exist in the Milky Way galaxy. Here's the formula:
N = the number of civilizations in our galaxy with which communication might be possible;There are various arguments about the Drake equation. Some argue for additional terms in the equation, others point out that the value of many of the equation's terms are fundamentally unknown. There's a reasonable argument to be made that "N" has to be a fairly low number, on the simple grounds that we have not yet detected any extraterrestrial civilizations. Depending on the assumed values of the terms in the equation, you can derive conclusions that range from the idea that we're alone in the galaxy (see the Fermi Paradox) to an estimate that there may be as many as 182 million alien civilizations awaiting our discovery (or their discovery of us).
R* = the average rate of star formation per year in our galaxy
fp = the fraction of those stars that have planets
ne = the average number of planets that can potentially support life per star that has planets
fℓ = the fraction of the above that actually go on to develop life at some point
fi = the fraction of the above that actually go on to develop intelligent life
fc = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space
L = the length of time for which such civilizations release detectable signals into space
From a fallacies basis, however, the problem comes when people argue that the vast number of stars makes it certain that alien civilizations exist. As much as I'd personally prefer to believe this, the logic here is fallacious. Probable — even highly probable — doesn't translate to certainty.
That's not an argument against the Drake equation per se, but merely a problem with an extreme conclusion drawn from it. The Drake equation was never intended to be science, but rather a way to stimulate dialogue on the question of alien civilizations.