[Osx-nutters] The separation of church and state.

[Mark Smith]

On 04.12.2007, at 20:36, Jared Earle wrote:

> On Dec 4, 2007 7:19 PM, LuKreme <kremels at kreme.com> wrote:
>> Most people, and many mathematicians and scientists, claim that the
>> chances of you winning are 50-50 because previous events can't
>> influence the outcome, right?
>>
>> They're wrong.  You should switch as that gives you a much better
>> chance of winning
>>
>> That's why statistics and probability sucks.
>
> ...but it's all probability. The reason people get it so wrong is
> because they don't understand probability. Here's the simplest
> explanation of the Monty Hall Car/Goats problem:
>
> door - two doors
> (1/3)     (2/3)
>
> We can all agree with that simplest basic probability. You have a one
> in three chance of getting the good prize when you guess cold.
>
> Then, if you remove one of the doors on the right side by exposing it
> as not-a-car, the remaining door has to pick up that two-in-three
> probability.
>
> door - door
> (1/3)  (2/3)
>
> This problem is only counter-intuitive because someone already knows
> the outcome and acts on it.

If you are a real student of the monty hall problem (as I suspect you  
might be), you know that that is a bit of an over simplfication, but  
I'll grant that it serves the purpose well enough.

My point about counterintuitivity was about superficial  
counterinituitivity. Most people think that they know how such a  
system works, but intuitively, they are wrong. Less than one in ten  
intelligent adults arrive at the correct answer to the Monty Hall  
problem when they are confronted with it for the first time. About 1  
in 4 of this 90% can quickly be won over, by one of several simple  
ways of portraying the real probability issue (e.g. Jared's portayal  
above). About another 1 in 4 will take a *lot* of convincing. The  
remaining 50% refuse flat out to accept the "truth". I've often  
wondered what the correlation between "religiousness" and "getting"  
the Monty Hall problem looks like. I have my suspicions, but I admit  
they are unfounded.

Mark.