3 ms·
What I dislike about this question is the flavor text. It seems designed to mislead the reader by invoking their “realism node,” and then requiring them to susp
by millstone 13y ago
What I dislike about this question is the flavor text. It seems designed to mislead the reader by invoking their “realism node,” and then requiring them to suspend it.
From archgoon’s link:
> "This puzzle confounds people legitimately, however, because most of the ways in which you are likely to find out that X has at least one boy contain an implicit bias which changes the answer.”
Exactly right. The phrasing in the problem asks the reader to consider a particular scenario, not isolated facts. Consider what happens if you take the question at its word:
> If a person on the street says to you, "I have two children," what is the probability that they're both boys?
Hell if I know. Maybe one is a boy and the other is a grown man? Or maybe he has five children, BBGGG. “I have two children, both of which are boys” is technically correct if there’s two boys and three girls, right? Or maybe he’s just outright lying! How do I assign a probability to any of those?
Consider this phrasing instead:
“If you flip a coin twice, and the first and/or the second is heads, what’s the probability that both are heads?” I’d expect more people to get this right than the boy/girl question.
Also, as an aside, punctuation is important:
“I have two children. At least, one of them is a boy.”
(Yikes!)
- heyitsnick 13y ago"I met a man on the street, he said he had two children. I asked him, is at least one of them a boy? He said yes. What's the probability both of them are boys?" This removes the whole ambiguity of why he would assert "at least one of them is a boy," but still makes the question a bit tricky/counter-intuitive, which is useful for teaching the quirks of probability.