>>11333459In case one, there are 4 equally likely possibilities:
1) Older girl, younger girl. Older girl answers door.
2) Older girl, younger girl. Younger girl answers door.
3) Older girl, younger boy. Older girl answers door.
4) Older boy, younger girl. Younger girl answers door.
In 2 out of 4 of these scenarios the other child is a boy, so the answer to (i) is 1/2.
In case two, there are 3 equally likely possibilities. This is not the same as in the first scenario because we know that the eldest child is a girl, eliminating possibility 4. This leaves:
1) Older girl, younger girl. Older girl answers door.
2) Older girl, younger girl. Younger girl answers door.
3) Older girl, younger boy. Older girl answers door.
In 1 out of 3 of these scenarios the other child is a boy, so the answer to (ii) is 1/3.
