Probability

I'm trying to teach myself probability, but it's really difficult for me to understand.

I'm trying this question from a textbook I've downloaded online, and I just can't seem to wrap my head around it.

Question 1. a) There is a family of 3 children. You saw one of the children, and it's a girl. What's the probability that all of them are girls?

1. b) You saw another child. You're not sure if it's the same girl you saw. What's the probability that all of the children are girls? Is it the same as question 1. a)?

For the first question, 1/7

A family having three children has a 1/8 probability of getting three girls
and a 1/8 probability of not having *any* girls
Therefore if one of them is known to be female and you have no information on the others then we can eliminate the situation in which they are all male, leaving seven possibilities. Only one of these is that all three are girls. There is a 1/7 chance.


The second is more complex. There's a 2/3 chance that the new person is a different girl, and therefore the three situations in which two children are male can be eliminated, leaving four remaining. This means there is a 2/3 chance that there is a 1/4 chance.
there's a 1/3 chance that you have no new information. This will have a 1/7 chance.
This means your total probability is :
(2/3)*(1/4)
+
(1/3)*(1/7)
= 1/6 + 1/21
=27/126

I probably got something unimportant like the actual numbers wrong, but that's pretty much it.
en.wikipedia.org/wiki/boy_or_girl_paradox