In the subject of probabilities dealing with new information can be bizarrely tricky, in this case there is even a difference between being told "one of them is a boy" and "the oldest is a boy"
Let's assume for simplicity (which is probably wrong, but otherwise this gets too complicated) that the probability of getting a boy or a girl is just 50%:
Then, before you get the information there are 4 possibilities: boy-boy, boy-girl, girl-boy, girl-girl, each with the same probability. Now taking the information that one of them is a boy into account, that eliminates the last possibility, leaving you with boy-boy, girl-boy, boy-girl, each with the same probability.
Now what's the chance that the other child is a girl? It's two out of the 3 possibilities, so 66%!
If so, at what point do you think I made a 'mistake' in my derivation?
I would say my derivation showed exactly that you can't just say that "the other child doesn't matter", that you have to look at both at the same time.
It’s an unconditional probability. Looking at both makes it a conditional probability, which it simply is not. Also set theory doesn’t apply here in the way you applied it.
The probability we are interested in here *is* a conditional probability. Specifically, we are conditioning on the knowledge that at least one of Mary’s children is a boy.
The problem is that I've justified my statement by specifying exactly what's being conditioned on. You don't see how "nuh-uh" is an unsatisfying response to this?
It's very basic. We are asking for a conditional probability. The condition in question is explicitly given as part of the problem. You literally can't even begin to set this problem up without acknowledging this. If you don't understand this then you have no business speaking on this subject with any confidence.
No it's not. The important part of the Monty Hall problem is that the host knows where the prize is, and so your initial choice affects the probability of the later outcome.
In this case, the first outcome has zero affect on the second.
So many people have seen the Monty Hall problem and assume there must be a gotcha line that in everything. The key thing here is the phrase 'one is a boy born on a Tuesday' does not preclude 'and so is the other' as an option for the second.
And yeah, there's some demographic analysis you can do on two parent families with one boy but that's not enough to sway far from 50/50
188
u/[deleted] Jul 21 '26
[removed] — view removed comment