[ExI] Probability mind benders [was: Psi and EP]

[John Clark]

On Jul 5, 2010, at 12:56 PM, mail at harveynewstrom.com wrote:

>> Now I tell you that I have 2 children and one of them is a boy born on a Tuesday.
> 
> Ambiguous in english.

It's ambiguous only in the sense of being incomplete, it does contain clear and valuable information even if not as much as we'd like. Almost everything scientists study is ambiguous in that way, that's why they use probability so much. 

And probability can be massively counterintuitive even for great minds. No less a mathematician than the great Paul Erdos got the Monty Hall Problem wrong. For a surprisingly long time he kept insisting that it can't be true. Eventually his colleagues did convince him that it was correct, but even then he felt dissatisfied and vaguely depressed; he knew it was true but it still didn't feel true.   

>  Does it mean that only one child is a boy?

Answering that question is the entire point of the exercise, is there one boy or two, and we can't know the answer with certainty but there are useful indications we can use, indications obtained by those "ambiguous" statements. We know for sure one one kid is a boy, perhaps 2 perhaps not. We don't know but we can make an educated guess and that's what probability is all about.

> The people who calculate this "wrong" are mathematically correct for the
> question they think they are being asked.  When the question is asked
> clearly, nobody calculates it wrong.

I have no idea what that means.

> This is not an example of non-intuitive statistics.

Well, there is the old chestnut about picking 23 people at random and finding that there is a greater than a 50% chance that two of them were born on the same day of the year, but I don't think it's quite as good, it's a bit easier seeing how that would be true.

  John K Clark





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