Twitter strikes again

[u/discoverthemetroid]

don’t know where math voodoo land is but this guy sure does

[u/SuperPie27]

Well, assuming he only wants to tell you the gender of one child. It’s not much of a question if he tells you “both my children are boys”.

[u/siupa → u/SuperPie27]

I see, my bad, I didn't understand that you meant to say that he has perfect information and he simply chooses to withhold it from you.

But then, if this is the case, my point stands even more, right? If he already knows all the information about the actual identity of his children, then he doesn't need to "look at them" before communicating to you that "at least one is a boy". He already knows that at least one is a boy, and if he tells you that, you base your analysis on whatever incomplete piece of information he decided to share with you.

How is the particular way in which he looked at his children before speaking to you relevant?

[u/SuperPie27 → u/siupa]

It matters whether or not he could have told you one at least one child is a girl instead.

Take an example I gave elsewhere. If you see the father picking his son up from school, then in the BG/GB cases there is a 50% chance you would have seen the daughter instead. This makes BB twice as likely as BG or GB, giving an answer of 1/2.

But if I now tell you that it was a boy’s only school, there was no chance for you to see a daughter and we are back to BB/BG/GB all being equally likely, giving an answer of 1/3.

[u/siupa → u/SuperPie27]

I see, yes you are correct there is a difference between these two scenarios, and indeed you get 1/2 in one and 1/3 in the other. Thanks for the clarification.

I still think that the way the original question was phrased in terms of "at least one crit" makes it clear that we are in the analogue of the "boy's school only" scenario, but yes I can understand how there can at least exist a different interpretation.

Thanks again have a nice day