Probability is much less meaningful when you're not talking about large groups of repeated trials.
In the context of the article, imagine that you didn't do this just one time, but that you asked 100 fathers about the compostion of their children.
The question posed in the article is essentially, "Of those fathers who responded 'I have one son,' (which is likely 75 of the 100), how likely is it that they have another son, (which is likely 25 of that group of 75, or 1/3).
When the article talks about the father standing next to one of his children at random and the probability of another son being 1/2 at that point, it helps to imagine those same 100 fathers all standing next to their children. Of that group, you're not eliminating the fathers standing next to girls based on the way the situation is posed.
The English words used to describe each case make it much less clear which group of 100 people we're talking about.
Also, when we talk about one father and not a group of fathers, the 1/3 or 1/2 number is much less meaningful. This is where insurance companies make their money (ideally). It's impossible to predict whether a single person will die in a car accident over their lifetime, and any number is essentially a guess. But it's very easy to predict that, say, 1 in 50,000 people will.
In the context of the article, imagine that you didn't do this just one time, but that you asked 100 fathers about the compostion of their children.
The question posed in the article is essentially, "Of those fathers who responded 'I have one son,' (which is likely 75 of the 100), how likely is it that they have another son, (which is likely 25 of that group of 75, or 1/3).
When the article talks about the father standing next to one of his children at random and the probability of another son being 1/2 at that point, it helps to imagine those same 100 fathers all standing next to their children. Of that group, you're not eliminating the fathers standing next to girls based on the way the situation is posed.
The English words used to describe each case make it much less clear which group of 100 people we're talking about.
Also, when we talk about one father and not a group of fathers, the 1/3 or 1/2 number is much less meaningful. This is where insurance companies make their money (ideally). It's impossible to predict whether a single person will die in a car accident over their lifetime, and any number is essentially a guess. But it's very easy to predict that, say, 1 in 50,000 people will.