I was asked the question “a man states he has two children, and at least one of them are boys, what are the odds that the man has two boys?” I’ve been told the answer is 1/3, but I can’t wrap my head around it. Additionally, there is another version of the problem that states he has at least one boy born on a Tuesday. How does that change the odds? Why?
Edited to add (so people don’t have to sort through replies): the answer is 1/3 because “at least one boy” is accounting for B/G & G/B. The girl can be the first or second child. You can move the odds to 50/50 by rewording the question to “my first of two children is a boy, what are the odds the other child is a boy”
In: Mathematics
Its a classic problem that I despise becuase it requires an additional bit of information that isn’t stated, and logically shouldn’t be assumed, but has to be assumed to get the answer to be 1/3.
That additional info is that despite being the father and despite having the knowledge that at least one child is a boy the father for some silly reason has no clue whatsoever which one of the children that is.
That is a necessary extra bit of info in order for it to not be 50%. The sensible interpretation of the meaning of the father saying “at least one is a boy” is that the father can point to one of the children and say “That one. That’s the one I know is a boy. I’m not sure about the other one.” That would mean “The gender of one child is locked down and thus no longer one of the variables. There is only one child with unknown gender left.”
The only way you get 1/3 is if the father meant “Oh, I know the gender of one of them but I still have no idea which of the two children is the one I know.” (Which is utterly bizarre and makes no sense at all as a way to picture the scenario.)
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