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The latest entry in the “Centauri Dreams” website:
https://www.centauri-dreams.org/
discusses a Bayseian statistics analysis of the probability of intelligent life in the cosmos They point to this video for a more detailed exposition of the problem:
https://www.youtube.com/watch?v=iLbbpRYRW5Y
I can barely follow the math here, and I’m not sure I believe it, so you might want to check it out for yourself.