Mark Galecki writes
>First, I realize that in my previous message (Re: I disagree with Lee's
>answer), I was a bit disrespectful of Lee's views. I apologize.
Okay, let's take a look at what Mark thinks that he has to apologize for:
>> ***Answers*** For problems 1, 2, and 3, the answer is 2/3. For...
> I disagree with this one. (As you see I am trying to be diplomatic here.)
> First, one of course assumes that sexes are equally probable (they aren't),
> otherwise this would not be an interesting little problem.
> One has to be careful about formulation of the problem. Lee wants to ask
> "given that there is at least one girl, what is the probability that there
> is one boy and one girl". The answer to this is of course 2/3, just as Lee
> claims.
> However, this is not what Lee is really asking. Note the pair of phrases:
> "one", and "the other". What the father is really asking is "I have picked
> one of my children (not necessarily at random). That child is a girl. What
> is the probability that the other child is a boy". To this question the
> answer is 1/2.
So what on Earth does Mark feel that he should apologize for? Even
his second statement, "As you see I am trying to be diplomatic here."
struck me as odd. In retrospect, I should have realized that Mark has
much higher standards of politeness than I do. I think that he was
reluctant to come out and say, "You're wrong, because....".
>However, Lee, instead of pointing it out [i.e., that I, Mark was
>disrespectful] (which is the best course of action in such cases),
>responds in kind...
>Lee, your long argument in favour of your answer is not needed.
>I don't need your "help". Of course I saw your argument immediately.
Of course. But perhaps you should think of others on this list
who aren't as mathematically sophisticated as you are. It wasn't
wrong of me to provide a very thorough explanation, (in order to
cut down on unnecessary misinterpretations and misunderstandings).
I'm sorry that it offended you.
>my message carefully, you will see I said [that the answer was 2/3]
>Anybody with common sense or probability training or intelligence,
>will quickly arrive at this answer.
This isn't true. (Sorry for being blunt.) Eliezer Yudkowski wrote
> I don't think your word problems provide the necessary
> priors. To estimate the probabilities, I would need to
> know the algorithms used by each of the people making
> statements, and that information is not provided.
and that's a sensible point of view, even for someone with
"probability training and intelligence". The problem is
deliberately tricky and provocative, and debates about it
can bring out some interesting points. I think that is fun.
>This list is comprised of people who want to preserve their
>thinking, therefore there must be something worth preserving,
>and so questions such as these are not "fun" as you claim,
>but boring - in my humble opinion.
I entitled the thread "Fun With Bayes' Theorem", because I
thought some would find those problems entertaining. But if
those problems were as boring as you say, it's interesting
that you responded to them. :-)
Now, I want to fully apologize for responding to you as I did
when I wrote "The flaw in your argument is...", because it was
unnecessarily condescending. It was even a worse gaffe because
you, Mark, had already given me hint that you adhere to a very
high standard of politeness.
On the other hand, if you expect people to say "I think that you
may be mistaken" when the truth is that they think that you are
dead wrong, then you are going to be very often offended. But
the whole question of how to go about being decently polite in
email is still open, in my book.
Lee
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