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
Two kids; one boy. So we only care about the other child; 50/50 odds boy or girl. So it’s common to say 1/2 odds that they are both boys.
Except we are actually looking at a variant of the Monty Hall problem.
Initially, looking at two kids; independent odds of gender, so four possibilities:
boy, boy;
boy, girl;
girl, boy;
girl, girl;
So 1/4 odds that you got “boy, boy”.
At least one boy; so remove the girl, girl option.
So 1/3 odds for “boy, boy” from the remaining options.
Unless there’s more in the second question, day of week wouldn’t matter at all.
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