3 ms·
Wait, explain it to me like I'm 10 years old. As I see it, there are three options - either it's a boy-boy pair, a girl-girl pair or a boy-girl pair. Now, sinc
by Sandman 13y ago
Wait, explain it to me like I'm 10 years old.
As I see it, there are three options - either it's a boy-boy pair, a girl-girl pair or a boy-girl pair. Now, since OP introduced the age variable, let's give the kids names to make things easier to understand. Let's say that the boys are named John and Jack, the girls Jill and Judy and if it's a boy-girl pair then they're named Jack and Jill.
Now if it's a boy-girl pair, we have exactly two options:
either Jack is older than Jill or Jill is older than Jack. This is shown in the first picture.
However, we also have two options for boy-boy and girl-girl pairs: Either Jack is older than John or John is older than Jack. Either Jill is older than Judy or Judy is older than Jill. This is not shown.
Since we know that one of them is a boy, we can dismiss both girl-girl pairs. Now we're left with four options. In 50% of these options the other child is a boy.
What am I missing?
- brazzy 13y ago> As I see it, there are three options - either it's a boy-boy pair, a girl-girl pair or a boy-girl pair. Yes, but those three options are not equally likely. Let's say the parents decide that their firstborn will be named Jack if male and Jill if female, and the second child will be John if male and Judy if female. Now you see that there are four possibilities: Jack+John, Jack+Judy, Jill+John, Jill+Judy. The last one is eliminated when you know that there is one boy, which gives 1/3 chance that it's the first.
- ajanuary 13y agoThe reason age was introduced was simply was a way of differentiating the two children (giving them identity). You introduced names to differentiate the two children, which is another perfectly good way to do it. But then you _also_ introduced age. Because you now have two different ways of labelling the children, you've introduced a new variable, and that changes the probability. A better way to look at it is with two unisex names: Drew and Sam. This completely replaces the age thing as a way of identifying them, so forget all about age. Our possibilities are: Drew: boy, Sam: boy Drew: boy, Sam: girl Drew: girl, Sam: boy Drew: girl, Sam: girl We know Drew and Sam can't both be girls, because at least one is a boy, so that leaves: Drew: boy, Sam: boy Drew: boy, Sam: girl Drew: girl, Sam: boy There's a 1/3 chance that both Drew and Sam are boys.
- Sandman 13y agoOk, yes, I get it now :). Thanks for the explanation.