What’s your justification for having P(she says “at least one is a boy” | 1B,1G) = P(she says “at least one is a girl” | 1B,1G)? Maybe the hypothetical mathematician is from a culture that considers it important to have at least one boy. (China was like that, IIRC)
As a twin, I always found it surprising how easily people assume that children’s genders are independent. I saw it more like ‘Kid1’<-‘Fertilization specifics’->‘Kid2’, and if, as Wiki says, monozygotic twins occur in about 3 cases per 1000, and same-sex dizygotic twins occur in half cases of all dizygotic twins1, then it’s not at all obvious that two children of the same mother have the same distribution of possible genders as two children of the same father or two random children at all.
1 - Wiki doesn’t state the frequency of dizygotic twins.
What’s your justification for having P(she says “at least one is a boy” | 1B,1G) = P(she says “at least one is a girl” | 1B,1G)? Maybe the hypothetical mathematician is from a culture that considers it important to have at least one boy. (China was like that, IIRC)
As a twin, I always found it surprising how easily people assume that children’s genders are independent. I saw it more like ‘Kid1’<-‘Fertilization specifics’->‘Kid2’, and if, as Wiki says, monozygotic twins occur in about 3 cases per 1000, and same-sex dizygotic twins occur in half cases of all dizygotic twins1, then it’s not at all obvious that two children of the same mother have the same distribution of possible genders as two children of the same father or two random children at all. 1 - Wiki doesn’t state the frequency of dizygotic twins.