If the statement “each family continues having babies till they have a boy” is true the ratio of boys to girls must be less than 0.5 if there is a 0.5 probability that a child born to a family is a boy.

Surely, if a probability tree is used the workings are;

Of each 1 family ;

=> 0.5 families have a Boy and STOP having children

=> 0.5 families have a Girl, continue having children and of each of these families;

=>> 0.25 families have a Boy and STOP having children

=>> 0.25 families have a Girl, continue having children and of each of these families;

=>>> etc, etc

So, if if the maximum number of boys a family can have is 1 and the maximum number of girls a family can have is infinite (as they do not stop until they have a boy) how can the ration of boys to girls ever be 1:1?

In fact, using infinity as the maximum number of girls per family, the result must *tend* towards a ratio of 0:1 !!

Can anyone explain why the logic above is incorrect?