So if the girl is the first child, the possibilities are:
or 1/2 the time the second child is also a girl
If the girl is the second child, the possibilities are:
or 1/2 the time the first child is also a girl
since the first scenario results in 1/2 and the second scenario results in 1/2, we have:
(50% * 1/2) + (50% * 1/2) = 1/4 + 1/4 = 1/2
Thus, like many have said - the odds are clearly 1/2 that the other child is also a girl.
Doesn't work that way. Why on Earth are you multiplying 50% by 1/2 twice and adding them together?
If you think your answer is logical and correct, PLEASE do the experiment with pennies that I laid out several times. When all TT combinations are removed, about 1/3 of the pennies will be HH, 1/3 will be HT, and 1/3 will be TH.