Not sure if this is the correct site on Stack Exchange to ask this, please let me know if there is a better one.
If civilizations were distributed fairly evenly in the habitable region of the galaxy, how many civilizations would there have to be for us to be able to detect at least one, assuming all civilizations had approximately the same level of science as us. (i.e. How many of "us" would there need to be for us to be able to detect one of "us")
There are some assumptions that I'm making that may be incorrect:
- The habitable region of the galaxy is not the entire galaxy. I believe the center of the galaxy is deemed to be uninhabitable due to the levels of radiation, but I'm unaware of other regions are considered uninhabitable, or how large this region is.
- It's generally only possible to detect another civilization from their broadcast emissions, which would probably limit detection range to somewhere around 50 LY or less.