Maths problems (interesting ones)

[Astronouth7303]

Originally Posted by FizMan

But I don't know... I honestly don't agree with your teacher's logic... yes I agree that the gender of one doesn't influence the gender of the second... but she seems to ignore the fact that there are twice as many families with a boy and a girl than there are with two girls.

Of course there is. GG, GB, BG, BB. But that assumes you can identify A and B. But in this instance, you can only identify them by which one opened the door, so you have to account for both instances. A or B may open the door!

A opens:
+GG
+GB
-BG
-BB
B opens:
+GG
-GB
+BG
-BB
It's still 1/2, 50-50.

Also, That list is generated from the combinations of 2 mutually exclusive chances, a table:

  B  G
B BB GB
G BG GG

The bottom line is: THE RESULT OF ONE DOES NOT AFFECT THE RESULT OF THE OTHER.