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.
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.
This is also confusing to me, as the resulting “probabilities” do not add up.
Read “having an index” as “having some specific index”, e.g. 42.
The probabilities add up because typed 1,2,3,4 are each probability 1⁄4 in total.