Posted by gbakker on 3/20/2013 8:28:00 PM (view original):
Here's what I see as the fault in your logic, pinotfan: I already know that one child is a girl, but that doesn't matter, it could be a boy. All I know about the other child is that it is either a girl or a boy, a population of two, either g or b. odds are 50-50 either way. If the child is a girl , the possible combinations are not gb,bg, gg, they are gb, gg.
It's 50-50 only if you're trying to predict a future event. That is not the case here as you are looking at results.
If you play craps, perhaps this will help. When you roll two dice, there are eleven different possible numbers you can roll, anywhere from two to twelve. However, there are 36 different outcomes:
Die 1 Die 2
2 4 etc.
So let's say I tell you I rolled a four. There are three ways to do that: 1-3, 3-1, and 2-2 - two possible combinations, but three ways to roll them. So, the odds of the combination being a one and a three, regardless of order, are 2-1. However, if I tell you one of the die rolled was a one, there is a 100% chance that the other number is a three. Knowing part of the existing data set has a direct impact, just as knowing the sex of one of the children.
Perhaps this site can explain it better: