I did enjoy the program on BBC4 last night The Search for Life: The Drake Equation. If you can use I-player then I suggest you go take a look. But what is the Drake Equation? This explanation lifted from SETI lays it out nicely:
Is there a way to estimate the number of technologically advanced civilizations that might exist in our Galaxy? While working at the National Radio Astronomy Observatory in Green Bank, West Virginia, Dr. Frank Drake conceived a means to mathematically estimate the number of worlds that might harbor beings with technology sufficient to communicate across the vast gulfs of interstellar space. The Drake Equation, as it came to be known, was formulated in 1961 and is generally accepted by the scientific community.
N = R* fp ne fl fi fc L
N = The number of communicative civilizations
R* = The rate of formation of suitable stars (stars such as our Sun)
fp = The fraction of those stars with planets. (Current evidence indicates that planetary systems may be common for stars like the Sun.)
ne = The number of Earth-like worlds per planetary system
fl = The fraction of those Earth-like planets where life actually develops
fi = The fraction of life sites where intelligence develops
fc = The fraction of communicative planets (those on which electromagnetic communications technology develops)
L = The “lifetime” of communicating civilizations
Frank Drake’s own current solution to the Drake Equation estimates 10,000 communicative civilizations in the Milky Way. Dr. Drake, who serves on the SETI League’s advisory board, has personally endorsed SETI’s planned all-sky survey.
Moving no from the Drake Equation you then get to the Fermi Paradox:
The Fermi Paradox is the apparent contradiction between the high probability extraterrestrial civilizations’ existence and the lack of contact with such civilizations.
In this program, I like how these two are covered. Consider how much of the EM spectrum there is to cover, how much our usage of radio has changed in just a few decades (AM to FM for example). Consider too a simple calculation: 100 billion (the number of stars in our galaxy) divided by that number of civilizations above.