[muyyatin]

I'll bite.

For the 1st question, you are drawing only from families with boys (excludes families with 2 girls). Only a 1/3rd of picked families would have two boys, so 2/3rds have the girl as the other child.

For the 2nd question, if you are asking about whether Joseph's sibling is a girl, I think more information is needed.

How is the child named Joseph picked? If we assume that a random boy (regardless of family) is chosen to be named Joseph, 1/2 of boys have male siblings and 1/2 have female siblings (the boy-boy situation is double-counted if choosing a random boy), so it would be 1/2.

If we named Joseph by choosing a family with at least one boy and naming one of their boys "Joseph" randomly, you get the same 2/3rds as the 1st problem.