Assume that every couple can only have exactly 1 child or two children, with those outcomes being equally likely. Ignore any silly extra factors (e.g. 1 child dying, another being alive).
If I choose a human on the face of the earth randomly, what is the probability that they had a sibling?
As a follow-up, what would be the general answer if couples had $i$ children with probability $\pi_i$?
My thought for the simple case is either 1/2 or 2/3, and I can think of compelling reasons for both.
Siblings get counted twice, and only-children get counted once, leading to 2/3.
A given person's parents were equally likely to give him a sibling or not, leading to 1/2.
This kind of problem occurred to me one day. A similar problem occurs to me when I think about divorce rates. (e.g. if the divorce rate is 50%, is the probability a person is divorced 50% or 66.6%?) Any help is appreciated!