Conditional on being in a billion-human universe, your probability of having an index between 1 and 1 billion is 1 in 1 billion, and your probability of having any other index is 0. Conditional on being in a trillion-human universe, your probability of having an index between 1 and 1 trillion is 1 in 1 trillion, and your probability of having any other index is 0.
Ehm.. Huh? I would say that:
Conditional on being in a billion-human universe, your probability of having an index between 1 and 1 billion is 1, and your probability of having any other index is 0. Conditional on being in a trillion-human universe, your probability of having an index between 1 and 1 trillion is 1, and your probability of having any other index is 0. Also, conditional on being in a trillion-human universe, your probability of having an index between 1 and 1 billion is 1 in a thousand.
That way, the probabilities respect the conditions, and add up to 1 as they should.
SSA first samples a universe (which, in this case, contains only one world), then samples a random observer in the universe. It samples a universe of each type with ¼ probability. There are, however, two subtypes of type-1 or type-2 universes, namely, ones with nuclear extinction or not. It samples a nuclear extinction type-1 universe with ¼ * 99% probability, a non nuclear extinction type-1 universe with ¼ * 1% probability, a nuclear extinction type-2 universe with ¼ * 10% probability, and a non nuclear extinction type-2 universe with ¼ * 90% probability.
This is also confusing to me, as the resulting “probabilities” do not add up.