How this calculator works
The model assumes two independent children with the same boy probability. Filtering families that contain a boy retains BB, BG and GB. Learning the sex of a specified child instead leaves the other child unchanged. In the marked version, filter families containing at least one boy with an independent attribute, such as a uniformly modelled weekday. This is a probability puzzle model, not a model of individual family biology or a method of predicting a child.
Formula
At least one boy: P(BB | at least one B) = p/(2 - p). Specified child: P(BB | that child is B) = p. At least one marked boy: P(BB | marker) = p(2 - t)/(2 - pt).
Worked example
For p = 1/2, the at-least-one rule gives 1/3 and the specified-child rule gives 1/2. If the marker has independent probability 1/7, the marked-family rule gives 13/27.
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Frequently asked questions
Does a parent volunteering information follow these rules?
Not necessarily. What a parent chooses to say can depend on both children. A reporting protocol is needed to assign the conditional probability.
What is the marker?
An independent attribute assigned to each child. The marked rule filters families containing at least one child who is both a boy and has that attribute.
Why does a specified child give one half in the fair model?
The information fixes one child. Under the independence assumption it gives no information about the other child.