ETIS -- extraterrestrial intelligent species
Operational definition of intelligent is "capable of communicating via radio"
Probability of finding ETIS -- 2 schools of thought
Cosmological principle -- makes the assumption of mediocrity. We live in an average "neighborhood" in the universe. There is nothing special about our location or time in history or conditions that make life possible. Therefore, one would expect to find similar conditions (and life) elsewhere in the universe.
Anthropic principle -- assumes that we exist because of very special conditions in our "neighborhood." Therefore, what we observe in our part of space is not typical of the universe as a whole, and so we shouldn't expect to find life elsewhere.
Note that both of these principles implicitly assume that ETIS would have certain similarities to us. Removing that assumption complicates these arguments somewhat.
Drake Equation (aka Greenbank Equation)
Developed by Frank Drake (at the Greenbank Observatory) in the 1960's
Tool for examining effects of various assumptions on the estimate of number of ETIS in our galaxy (but it can be applied to any part of the universe)
N = R P E L I C T
[numbers in brackets below indicate permitted values to use in the equation]
N = number of ETIS in our galaxy
R = rate of star formation [number/year]
Our galaxy (Milky Way) is about 10 billion yrs old and contains about 100 billion stars, so R = 10 stars/yr is the standard assumption
P = fraction of stars with planets [0-1]
E = environmental factor = number of planets in a solar system that are ecologically suitable for life [0-?]
L = fraction of planets with suitable environment where life actually did develop [0-1]
I = fraction of inhabited planets where intelligent life-form evolves [0-1]
C = fraction of planets with intelligent life that has developed radio communications [0-1]
T = time [years] that a technically developed civilization survives
Values used in the equation are somewhat subjective.
examples
optimistic outlook
R = 10, P = 1, E = 5, L = 1, I = 0.1, C = 1, T = 5000 yrs
N = 25000 ETIS
conservative outlook
R = 10, P = 1, E = 1, L = 0.1, I = 0.1, C = 0.2, T = 100 yrs
N = 2 ETIS