RE: math question verrrrrry off topic
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 > >>>>> _______________ > >>>>> > >>>>> > >>>>> > >>>>> > >>>> > >>>> > >>>> > >>>> > >>> > >>> > >>> > >> > >> > >> > > > > > > >
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