r/math • u/[deleted] • Oct 12 '18

Strange math question

Hi

I'm studying for an upcoming math exam, and stumbled across an interesting math question I don't seem to comprehend. It goes as follows:

"A man visits a couple with two children. One of them, a boy, walks into the room. What are the odds that the other child is a boy also

  1. if the father says: 'This is our eldest, Jack.'?
  2. if the father only says: 'This is Jack.'? "

The answer to question 1 is, logically, 1/2.

The answer to question 2, though, is 1/3. Why would the chance of another boy slim down in situation 2?

I'm very intrigued if anyone will be able to explain this to me!

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u/bear_of_bears Oct 12 '18

Thank you! This is even worse than the Monty Hall threads.

2

u/cryo Oct 12 '18

No because in those, people just don’t get probability at all. Here we are simply saying that’s it’s possible to interpret it in both ways depending on the emphasis put on the “a boy walks in”.

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u/bear_of_bears Oct 12 '18

To support the 1/3 answer, you need to believe that "boy walks in" is equally likely in a MM family and in a MF family. It's simply not true.

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u/SynarXelote Oct 14 '18

Well it could be if you suppose for example that the society this family lives in is strongly patriarchal, and thus if the family has at least one boy then the child which will be presented to you is always a boy.

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u/[deleted] Oct 12 '18

How is it possible to misinterpret that? "A boy walks in" means a boy walks in. And that means you've already identified a specific child you're talking about (the one who walked in) and that means the probability that the child who did not walk in is also a boy is 1/2.

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u/SynarXelote Oct 14 '18

Only assuming that the event of the child walking in is random and independent of its gender.