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
I think the biggest mistake that people are making in visualizing the problem as a coinflip is considering the 2 flips to be of the “same” coin. This produces a false equivalence between the first and second child. If you call Heads girls, and Tails boys, and the first born is a Quarter, and the second born is a Dime. This becomes more obvious:
Heads Quarter, Heads Dime => GG
Heads Quarter, Tails Dime => GB
Tails Quarter, Heads Dime => BG
Tails Quarter, Tails Dime => BB
If you eliminate the HH combination, that leaves 3 possible outcomes for the father in the question. GB and BG cannot be conflated.
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