|
How embarrassing. I've just sneakily edited the question in the first message in this thread to fix the setup so that the answer I've given is right.
I was reading the comments over at New Scientist and realised that for much the same reason I disagreed with their answer to their setup for the final stage, I must also disagree with the other answer.
My original post had Dan stating "I have two children" and "I have at least one boy".
The first statement is OK, but for exact clarity hould have been (and now is)
"I have exactly two children".
The second statement doesn't work the way I wanted. I should have (and now have) turned it into a question by Nick and an answer of "Yes" from Dan. Here's why.
Consider a large set of fathers of exactly two children. They are all asked to make a statement of the form "I have at least one [boy | girl]". They can all do so. This doesn't mean that of the half that answered "I have at least one boy", only one third have two boys. Obviously on average half of that half have two boys, because 1/4 of the whole set has two boys.
In short, the answer at that stage is indeed 1/2 (as some said), not 1/3. Only if someone else asks the question and gets an affirmative answer does the probability become 1/3.
How very complicated. And how embarrassing that having spotted the problem with the second half of the New Scientist setup I failed completely to spot the problem with the first half.
|