Probabilty Riddles

[closer2313]

I can see how the answers are the answers, but I dont see exactly why. Can you guys explain?

Imagine you just won a TV-quiz, and the quiz master gives you the chance to go home with a car that is hidden behind one of three closed doors. The quiz master asks you to select door A, B, or C, and you select door B. Then, the quiz master opens door C, behind which no car appears to be present, and he asks you whether you want to stick to door B or to change to door A. What should you do?

Answer
Go to Door A because it is 66% while B is only 33%.

I can see that if door B was only 33% with 3 doors, and one door is eliminated that the other door would double, but why wouldn't both doors increase to 50%?

You are at the park, pushing your daughter on a swing. You meet a woman and start a conversation. She says she has two children. You ask if she has any girls. She says yes. What is the chance that both children are girls?

Answer 1/3
Possibily combinations of children with one girl is
BG,GB,GG
so GG is 1/3 but aren't GB and BG the same thing? I dont see why the order matters in this problem.

Thanks for any help.