I guess what confuses some people is the phrase “the other one” which sounds like denoting a specific (in terms of SSN) child while it’s not at all clear what that could even mean in case of two boys. I think step one when being confused is to keep rephrasing the puzzle until everything is well defined/clear. For me it would be something like:
My friend has two kids, and I don’t initially know anything about their sex beyond nation level stats which are fifty-fifty. She says something which makes it clear she has at least one boy, but in such a way that it just prohibits having two girls without hinting at all if these are two boys or one, perhaps something like “i have to pick up Johny from kindergarten”. How much should I bet she actually has two boys vs a boy and a girl?
The first sentence of that phrasing is great! It makes things much more clear. But:
“i have to pick up Johny from kindergarten”
actually would give the probability of the other kid being a boy a fifty-fifty chance still, I believe. I still think the clearest way to phrase that part of the puzzle is for the narrator to ask the woman “is at least one of your kids a boy?”.
I agree that my phrasing was still problematic, mostly because it seems to matter if she said something spontaneously or as a response to a specific question. In the first case, one has to consider how often people feel compelled to say some utterance in various life scenarios. So for example in case one has two boys the utterance “i have to pick up Johny from kindergarten” might have to compete with “i have to pick up Robert from kindergarten” and might be strange/rare if both are in similar age and thus both should be picked up etc. Still, I think that without knowing much about how people organize their daily routines, my best bet for the question “does she have two boys?” would be 33%.
I guess what confuses some people is the phrase “the other one” which sounds like denoting a specific (in terms of SSN) child while it’s not at all clear what that could even mean in case of two boys. I think step one when being confused is to keep rephrasing the puzzle until everything is well defined/clear. For me it would be something like:
My friend has two kids, and I don’t initially know anything about their sex beyond nation level stats which are fifty-fifty. She says something which makes it clear she has at least one boy, but in such a way that it just prohibits having two girls without hinting at all if these are two boys or one, perhaps something like “i have to pick up Johny from kindergarten”. How much should I bet she actually has two boys vs a boy and a girl?
The first sentence of that phrasing is great! It makes things much more clear. But:
“i have to pick up Johny from kindergarten”
actually would give the probability of the other kid being a boy a fifty-fifty chance still, I believe. I still think the clearest way to phrase that part of the puzzle is for the narrator to ask the woman “is at least one of your kids a boy?”.
I agree that my phrasing was still problematic, mostly because it seems to matter if she said something spontaneously or as a response to a specific question. In the first case, one has to consider how often people feel compelled to say some utterance in various life scenarios. So for example in case one has two boys the utterance “i have to pick up Johny from kindergarten” might have to compete with “i have to pick up Robert from kindergarten” and might be strange/rare if both are in similar age and thus both should be picked up etc. Still, I think that without knowing much about how people organize their daily routines, my best bet for the question “does she have two boys?” would be 33%.
It’s get funnier with “i have to pick up my younger one, John from kindergarten” :)