Two Girls

Here is another series of puzzles where more knowledge of the situation changes the odds, and even more knowledge changes the odds yet again.

1. There is a couple with exactly two children. What are the odds that both are girls?

2. The same as #1, but now you are told that one child is a girl. What are the odds that both are girls?

3. The same as #2, but now you are told that one child is a girl named Idhitri. What are the odds that both are girls?

For ease of calculation, assume the boy:girl ratio is 50:50 in the population.

I found these puzzles discussed in a very enjoyable book titled “Drunkard’s Walk” by Leonard Mlodinow. But I must warn you, discussing #3 with other people generates a lot of heat, just like what happened with the Monty Hall problem (http://www.marilynvossavant.com/articles/gameshow.html). Even after accepting the correct answer intellectually, it is not intuitively obvious.