Gonna give this a shot (without reading the previous commenter) so here goes, though I could be wrong, I hate conditional probability:
1. 25% 2B, 50% 1B1G, 25% 2G
2. At least one child is a girl, so the 25% BB case goes away. Thus, now it's 2/3 likely there's one boy and one girl, and 1/3 likely there are two girls.
3. 1/3.
4. Now you're making the kids distinguishable. The only possibilities are 50% GB and 50% GG, so it's 50% likely both kids are girls.
5. Same as 4. 50%.
6. I can't see how this is different from 5. You're still getting the same information, that the eldest is female, and that the gender of the youngest is still unknown (and equally likely to be boy or girl). So, 50% again.
7. I'd say this is the same case as 2. All you know is that there's one girl in the house, and the three remaining cases (GB, BG, GG) are equally probable. The odds that both children are girls is 1/3.
no subject
1. 25% 2B, 50% 1B1G, 25% 2G
2. At least one child is a girl, so the 25% BB case goes away. Thus, now it's 2/3 likely there's one boy and one girl, and 1/3 likely there are two girls.
3. 1/3.
4. Now you're making the kids distinguishable. The only possibilities are 50% GB and 50% GG, so it's 50% likely both kids are girls.
5. Same as 4. 50%.
6. I can't see how this is different from 5. You're still getting the same information, that the eldest is female, and that the gender of the youngest is still unknown (and equally likely to be boy or girl). So, 50% again.
7. I'd say this is the same case as 2. All you know is that there's one girl in the house, and the three remaining cases (GB, BG, GG) are equally probable. The odds that both children are girls is 1/3.