Testing random

[Steven D'Aprano]

On Mon, 8 Jun 2015 04:23 am, Thomas 'PointedEars' Lahn wrote:

> Chris Angelico wrote:
> 
>> On Mon, Jun 8, 2015 at 2:36 AM, Thomas 'PointedEars' Lahn
>> <PointedEars at web.de> wrote:
>>>> The greater the multiplier, the lower the chance that any element will
>>>> have no hits.
>>> Wrong.
>>>
>>>> [ex falso quodlibet]
>> 
>> Huh. Do you want to explain how, mathematically, I am wrong, or do you
>> want to join the RUE in my ignore list?
> 
> I already did; you have overlooked it.  In a nutshell, the probability of
> 
>   1 1 1 1 1 1 1 1 1 1 1
> 
> is *the same* as that of
> 
>   1 2 3 4 5 6 7 8 9 1 2
> 
> and the same as that of
> 
>   8 3 6 3 1 2 6 8 2 1 6.

True, but irrelevant. What is irrelevant is that the probability of:

    1 1 1 1 1 1 1 1 1 1 1

is MUCH LESS than the probability of:

    1 2 3 4 5 6 7 8 9 1 2  or
    8 3 6 3 1 2 6 8 2 1 6  or
    9 3 1 5 5 4 7 1 6 8 1  or
    2 3 3 1 8 9 7 2 5 1 6  or
    7 8 9 4 2 7 7 1 3 8 2  or
    ...
    [enumerate millions of other possibilities]
    ...
    2 1 5 5 8 1 8 7 6 5 1 or
    3 4 9 5 2 8 4 2 3 2 6.


> So, I am sorry to tell you this, but you do _not_ understand probability.

It's certainly true that you don't.

> And you *cannot* understand it intuitively, like you tried to. 

Rubbish. Chris has got it right. Whether he did so "intuitively" or whether
he learned this after years of study is irrelevant, and you have no
evidence for which it is. You are jumping to wrong conclusions -- you are
so sure that you're so much smarter than everyone else that you've ASSUMED
that Chris must be wrong and *completely failed to pay attention* to what
he has actually said, responding to things he hasn't said.


> It is why humans play the lottery using their “lucky numbers” whereas
> other numbers have exactly the same probability of being drawn; 
[snip more irrelevant examples]

None of these things are relevant in the slightest.


> An extension of that misconception is emphasized by an anecdote (which may
> be apocryphal) told about Richard Feynman (I heard it from Lawrence Krauss
> in “A Universe from Nothing”; he can tell that in a much more funny way
> than I am able to reproduce it here [1]):
> 
>   Richard Feynman used to go up to people all the time and he’d say:
> 
>     “You won’t believe what happend to me today!
>      You won’t believe what happend to me today!”
> 
>   And people would say:
> 
>     “What?”
> 
>   And he would reply:
> 
>     “Absolutely nothing!”

And I wouldn't believe it either. *Something happened*. He got up. He put
his shoes on. He washed his face. These are all events, but they are not
memorable events. They are equivalent to a sample like:

    6 8 1 5 9 2 7 6 3 3 2

There are millions of ways to get a non-memorable sample like that, but only
nine ways to get a memorable sample like:

    2 2 2 2 2 2 2 2 2 2 2


Your mistake is that you are comparing that one memorable sample to any
*one* of the non-memorable ones, when you should be comparing the
probability of *any* memorable sample against *any* non-memorable ones.

Actually, your real mistake is hubris. *Nothing* in Chris' comments in this
thread should lead you to the conclusion he doesn't know what he is talking
about, but you're so full of the preconceived notion that he must be wrong
because he is not Thomas Lahn that you've actually made an astonishing
blunder and compounded it with laughable arrogance.



-- 
Steven