Re: math question verrrrrry off topic
This is (one reason) why casinos make so much money, because people
make the mistake of thinking the probability of the next throw
depends somehow on how the die has fallen on the last throw, but it
doesn't. No matter how many times you throw the die, and no matter
how the die has fallen before, the probability of a 1 on the next
throw is still 1/6.
On Jan 19, 2008, at 7:57 AM, Dave S wrote:
I must say that even in simple probability, the concept is a little
hard to
grasp for me. I can do the math, but to FEEL it is different.
Say I am throwing a dice now. The chance of getting a 1 is 1/6.
Let's say I
did get a 1. Now I am throwing again. I pick up the same dice and
make the
same random throw. On one hand I think everything is the same, so the
probability of getting 1 should still be 1/6. On the other hand, of
course,
chances of getting two 1's in a row is lesser, so the probability
is now
1/36.
If this is an exam in the statistics class, I can do the math and
pass, but
up to this day, my mind would still flip one way or another because
both are
making some sense to me. Isn't this weird?
Dave
-----Original Message-----
From: Katharine Thayer [mailto:kthayer@pacifier.com]
Sent: Saturday, January 19, 2008 9:52 AM
To: alt-photo-process-l@usask.ca
Subject: Re: math question verrrrrry off topic
Okay, look.
If this were a simple probability experiment, let's say there
were 600 objects in a big jar, all exactly the same size and
shape and differing only in color: 450 red ones (for
not-accepted) and 150 green ones (for "accepted") all mixed
up really well, and the question was, "if some people from
College X reached into the jar blindfolded and three of them
pulled out green objects, what would the probability of that
result be, would it be 1/4x1/4x1/4?" then the answer would
be "only if just three people from College X reached into
the jar. If more than three people from college x reached
into the jar, let's say five people from college x reached
into the jar, then the probability of three of those five
people pulling out a green marble would be 1/4 x 1/4 x 1/4 x
3/4 x 3/4."
But of course this isn't anything like that. In this case, the 600
objects in the jar are made by the people who are being
selected, and the objects are all different, all different
sizes and shapes and
colors, and made of different materials. People might contribute
different numbers of objects (though it's never been clear to
me whether that's the case or not) in which case the objects
made by the same person presumably aren't as different from
each other as the objects made by different people. And the
selection is made not by the people themselves reaching into
the jar blindfolded, but by a third party, a judge, who also
doesn't reach into the jar blindfolded and pull out objects
randomly to make a selection, but pours them all out on in a
big tray and looks at all 600 of them closely before
deciding which ones he/she wants to include. This particular judge
might be drawn to metal objects, or even especially to
platinum over silver, or maybe he or she particularly
dislikes street scenes and prefers pictures of old mills, or
is looking for a certain level of craftsmanship in the work,
or maybe the criterion is something even more difficult to
articulate, whether the judge "likes" something or not.
Whatever the criteria, by the end of the day, the objects are
separated into two piles, "accepted" and "not accepted," and
there are 150 objects in the first pile and 450 in the second pile.
I hope it should be clear to everyone at this point how
different this is from the problem above, and why you can't
treat this as a problem of simple probability and say that
the probability of any entry being accepted is the same as
the probability of any other entry being accepted, and that
this equal probability for each entry is 1/4, since 1/4 of
all the entries were accepted. It's just not
that kind of problem, and it doesn't work to treat it that way.
Thank you.
Katharine
On Jan 18, 2008, at 6:49 PM, Katharine Thayer wrote:
:--)
On Jan 18, 2008, at 6:23 PM, Diana Bloomfield wrote:
Hey Katharine,
I don't know-- maybe. I honestly didn't read the other
answers. :)
On Jan 18, 2008, at 8:43 PM, Katharine Thayer wrote:
Hmm, I thought that's what we all already have said, isn't it?
That that theoretical probability (1/4x1/4x1/4) would
hold only if
assumptions were met, and since assumptions are
obviously not met
(for example, judging is not a random lottery of course
but is done
on the basis of criteria, arbitrary or otherwise but
certainly not
random). Also, no one has said whether the 600 entries are 600
works or 600 people; I was assuming that they are 600 works
representing fewer than 600 people, in other words people could
submit more than one work, in which case, as I said, the
number of
works submitted per person would also have to be figured into the
equation somehow. Besides, if one person submits ten pieces and
another person submits one, the ten pieces by the one person
couldn't be considered independent entries in the same way one of
those ten could be considered independent of the one from
the other
person, and independence is also an assumption that must
be met in
order to consider the probability of acceptance to be the
same for
all entries.
Katharine
On Jan 18, 2008, at 4:25 PM, Diana Bloomfield wrote:
Okay, Chris. Here is it-- straight from my resident
statistician
here:
If they were the only 3 people from that institution who
applied,
AND if judging was completely random, then the
probability of this
is roughly 1 in 64 (key word: roughly). If more than
that applied
from this same institution, and only 3 got in, then the
calculation
will be more complex.
Hope that helps. :)
On Jan 17, 2008, at 12:00 PM, Christina Z. Anderson wrote:
Where else but this list can I ask these weird questions about
chemistry and math and computers and alt???
OK for you math people (Yves?): If there is a show and 600
entries, and 150 are accepted, there is a 1 in 4 chance of
acceptance. If 3 people from the same institution are accepted
what percent chance is that--is it 1/4 x 1/4 x 1/4 or a 1.5%
chance or is it a more complex formula?
Forgive the off topic request but it does relate to
photo as 3 of
our program got into a photo show and I want to be able to
mathematically brag about it to the dept. head/dean.
Chris
Christina Z. Anderson
Assistant Professor
Photo Option Coordinator
Montana State University
CZAphotography.com
_______________
|