[VedalkenBear]

Oh, I'm using the binomial not the hypergeometric. The binomial probabilities are simply the probabilities of a given number of sites in a province. These states are not dependent on one another. If the site placement algorithm checked for a first site, found none, and _did not check anymore_, that would be conditional probability.

Basically, for the second calculation you have:

0 sites in province (trivial case): 0
1 site in province (also trivial): 0
2 sites in province, 1 is earth, chance that the second is earth: Probability that there are two sites in province * 1-(Probability that the first is not Astral(1)*Probability that the second is not Astral(0.875) = 0.3456*(1-(1*0.875)

And so on. If the probabilities change given one state, that means the probabilities are conditional. The only way for that to happen in this case would be if the site search algorithm were to stop checking for sites if any check failed. That AFAIK does not happen.