TL;DR version: the use of Drake-like equations, with point estimates of highly uncertain parameters, is wrong. Extant scientific knowledge corresponds to uncertainties that span multiple orders of magnitude.
When the statistics is done correctly to represent realistic distributions of uncertainty in the literature, “people who take the views of most members of the research community seriously should ascribe something like a one in three chance to being alone in the galaxy and so should not be greatly surprised by our lack of evidence of other civilizations. The probability of N <10^−10 (such that we are alone in the observable universe) is 10%. ”
From the conclusions, when the priors are updated
When we update this prior in light of the Fermi observation, we find a substantial probability that we are alone in our galaxy, and perhaps even in our observable universe (53%–99.6% and 39%–85% respectively). ’