First, I know this riddle has been asked (many times) before. The question I want answering is why is a tree diagram not a correct method for determining the probability in this case.
There are two children, equally likely to be Boy or Girl. If we know one (or more) is a Boy, what is the probability that there is a Girl in the pair?
The sample space looks like this:
BB
BG
GB
GG - not possible
Therefore the probability is 2/3, but if I draw a tree diagram:
The probability of a girl in the pair seems to be $$\frac{1}{4}+\frac{1}{2}=\frac{3}{4}$$
Why does a tree diagram fail?