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
For those arguing 2/3, does this mean that of those that have 2 kids, one of which is a boy, that 2/3 of them have a girl.
It’s 50:50, which can be manipulated to 2/3 if you set some funky conditionals and phrasings, or you lock the background population (like the Monty hall problem). Birth gender is always a fun one for stats because the 50:50 is the only metric that impacts it. A good example of this is “does the 1 child policy (stop after 1 boy or repeat until you have one, impact gender ratios – no it doesn’t, always 50:50, reduced eventually cos women live longer unless there’s female infanticide, and that shows up on the stats very sharply.
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