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Hupp31
06-03-2010, 09:06 PM
I ran across this brain teaser and was going to dismiss it post haste. However, it struck me that this is a real life scenario that the military faces all the time. I'm guessing that some similar number crunching is going on with the oil spill in trying to calculate various probabilities and possibilities there.

I can hold my own up through Trig, but I'm still waiting for that damn train from Topeka to pass the one from Oshkosh somewhere near Mt. Rushmore. I don't even know how to begin the following as I always sucked at probability - unless the dice were loaded or the coin had 2 heads. Any thoughts?

***

You are the Intelligence Officer for a Special Ops unit planning to assault a terrorist hideout and rescue several kidnapped citizens of your country. Your Commanding Officer has asked you to calculate the probability that the kidnapped citizens will be released as a result of the assault.

Construct a probability tree considering the following:

1. The success or failure of the Special Ops Unit reaching the terrorist hideout.

2. An attempt by the terrorists (yes or no) to booby-trap the kidnapped citizens with explosives.

3. The killing of the kidnapped citizens (none, some, all) during the rescue attempt.

You have carefully analyzed the situation and determined there is a .9 probability of the Special Operations Unit reaching the terrorist hideout and a .3 probability that the Kidnapped citizens will be booby-trapped with explosives.

If the kidnapped citizens are booby trapped, there is a .4 probability that all will be killed during the assault, a .4 probability that some will be killed, and a .2 probability that none will be killed.

If the kidnapped citizens are not booby-trapped, there is a .6 probability that none will be killed, a .2 probability that some will be killed, and a .2 probability that all will be killed.

Calculate the total probability that all of the kidnapped citizens will be rescued, and provide any other finding you believe relevant.

***

I was fine until the part about the "probability tree" (third sentence). Is that anything like an oak or maple?

Would anyone out there dare hazzard a guess? How would one even begin to tackle this?

Thanks,

Phil

06-03-2010, 09:16 PM
Too long

Tony Ennis
06-03-2010, 09:38 PM
It's pretty easy actually.

So determine the probabilities, just multiply them together.

For example, the troops have a .9 probability of getting to the terrorist's hideout. There's a .3 chance the hostages are wired. That means there's a .27 chance the troops will arrive to find wired hostages. There's a .63 chance they'll arrive to find un-wired hostages. Then you repeat the method for the next layer of probabilities. Since there's a .27 chance of finding wired hostages and .4, .4, and .2 chance of all, some, or none of the hostages being killed, the chances of the events are .27*.4, .27*.4, and .27*.2 respectively, or .11, .11, and .05. So there's a grim 5% chance you'll get all the hostages out alive if they're wired.

Applying this to the unwired part of the problem, the final chances are .13, .13, and .38 for all, some, or none, respectively.

*assuming the wired and unwired situations are unrelated events*, you can sum the like results. So the chances of losing all the hostages is .11+.13 = .24. Same for some being killed .11+.13. However, getting them all out is a .05+.38 = .43 chance.

So if you do a single assault and you know nothing about the situation you can expect all the hostages to live 43% of the time. You'll lose them all 24% of the time. You'll lose some 24% of the time. 43+24+24 = 91 (rounding error, it's really 90) The reason it's 90 instead of 100 is because 10% of the time nothing happens - the troops get lost.

Again, this assumes the branches of the tree are independent. For example, say the troops get lost but the terrorists have spies that tell them the troops are in the area and they kill the hostages - those are no longer independent probabilities.

Regarding the .1 probability of the troops getting lost, I don't count this one way or the other since it doesn't help resolve the situation.

Now, if I were the commander, if the troops get lost, I'd sent them back in. They will eventually find the hideout. So the .9 probability would become 1 - a 100% chance of finding the hideout. The odds change because now we're multiplying by 1 instead of .9. In this case, all the hostages die 26% of the time, some die 26% of the time, and all live 48% of the time. Same proportions.

andy_b
06-03-2010, 09:50 PM
I'd like to know how they came up with the initial probabilities.

I agree with Tony's results. I didn't calculate it out, but his method would have been the one I followed.

andy b.

Mcgyver
06-03-2010, 10:23 PM
Phil, very easy Q if you draw it out as a decision tree...excel is excellent for this. Its more easy to get muddled without the tree. The become a usefull business tool, er sales tool, when there's differing dollar amounts at each decision point. Of course the probabilities are pulled from thin air but most won't argue with something as serious sounding as biz science....hence its main function is as a sales tool to get what you want :D

like this: http://www.treeplan.com/images/treeplan_large_2009-11-06_13-22-46.gif

dp
06-03-2010, 10:40 PM
I'd have just cracked open a Bud and waited for the 11:00 o'clock news. What's the rush?

Don Young
06-03-2010, 11:07 PM
I'd like to know how they came up with the initial probabilities.

I agree with Tony's results. I didn't calculate it out, but his method would have been the one I followed.

andy b.

In my opinion that is the problem with a lot of decision making. You can do wonderful things with mathematics but if the initial premise is wrong or of unknown accuracy, then so is the result, no matter how brilliant your calculations are.

I do understand this is a theoretical situation where the initial conditions are givens and are therefore assumed correct.

Don Young

gmatov
06-04-2010, 12:12 AM
I wouldn't give a nickle's worth of thought to any of their outcomes.

Life and death situations are not 24 Hours things.

"The Best Laid Plans of Mice And Men."

Thing do NOT go according to plan. That is why we are at Plan H or something with the Gulf Spill. Seems we will be getting to AA or BB or MM before the leak is fixed.

ALL of this was supposedly planned to prevent, tho' Transocean says it was denied by BP.

Cheers,

George

Tony Ennis
06-04-2010, 12:14 AM
Even when the probabilities are made up there's a value to it. Once they are on paper, they can be discussed and debated. They'll also tell which parts of the decision tree are more important than others so resources can be spent to determine more realistic estimates.

Evan
06-04-2010, 12:37 AM
Probability is a field where most people get lost immediately. It is not intuitive at all. If you flip a coin 10 time and it comes up heads ten times in a row then what is the chance of it coming up heads on the next flip?

It is still 50/50. The coin has no memory. That is a point that if very often misunderstood.

Another example is the Monty Hall Problem.

Imagine that the set of Monty Hall's game show Let's Make a Deal has three closed doors. Behind one of these doors is a car; behind the other two are goats. The contestant does not know where the car is, but Monty Hall does.

The contestant picks a door and Monty opens one of the remaining doors, one he knows doesn't hide the car. If the contestant has already chosen the correct door, Monty is equally likely to open either of the two remaining doors.

After Monty has shown a goat behind the door that he opens, the contestant is always given the option to switch doors. What is the probability of winning the car if she stays with her first choice? What if she decides to switch?

dp
06-04-2010, 12:46 AM
Probability is a field where most people get lost immediately. It is not intuitive at all. If you flip a coin 10 time and it comes up heads ten times in a row then what is the chance of it coming up heads on the next flip?

It is still 50/50. The coin has no memory. That is a point that if very often misunderstood.

A true probabilities wank would suspect a forcing of the results and bet the trend. Or at least he'd convince his customers to bet that way.

oldtiffie
06-04-2010, 05:24 AM
http://en.wikipedia.org/wiki/Probability

http://en.wikipedia.org/wiki/Statistics

http://en.wikipedia.org/wiki/Certainty

http://en.wikipedia.org/wiki/Confidence

http://en.wikipedia.org/wiki/Luck

http://en.wikipedia.org/wiki/Hope

etc.

Evan
06-04-2010, 07:39 AM
Tiffie,

Wikipedia is filled with trash. You cannot depend on what is posted there. It serves no purpose to post a bunch of links to what anybody on this site can look up if they are so inclined. If you want explanations for math questions try Wolfram Mathworld.

http://mathworld.wolfram.com/

oldtiffie
06-04-2010, 08:09 AM
Evan,

unless you can prove otherwise and conclusively that Wikipedia is full of trash (to the exclusion of all other as you say and infer) is pure subjectivity - which you, like anyone else, are quite entitled to have as they are to judge for themselves.

There was a lot of unsubstantiated and non-defined terminology being tossed around, so I decided to post a few links that I think are relevant and that others are able and free to assess for themselves and (to) use and add to - or not - as it suits them.

You, as are any others who choose to do so, are quite entitled to edit or seek to have Wikipedia items edited and revised and judged by you peers.

I look forward to the result of your contributions to Wikipedia.

I have used Wolfram before, and went to the link you posted and (then) to Wolframs Probability and Statistics links at:
http://mathworld.wolfram.com/topics/ProbabilityandStatistics.html

Perhaps, as it seems that you have endorsed Wolfram in that context, that you can show us - or me - where and in what ways Wolfram over-rides and contradicts the Wikipedia links that I posted.

I await your learned discourse which will - or should be able to - prove conclusively that Wikipedia is "filled with trash" - including the topics of probability and statistics which are the theme/s of this thread.

A.K. Boomer
06-04-2010, 08:22 AM
Im still laughing at Tiffers title, I tuned in this morning and in the general category it read "Waaay OT Late Night Head..."

I said to myself - wow --- this really is going to be Waaaaaaaay OT. :p

Evan
06-04-2010, 08:54 AM
Well, Tiffie, where to start?

Anti-Wikipedia 2: The Rise of the Latrines
by
Paulo Correa, M.Sc., Ph.D.
Alexandra Correa, H.BA.
ISBN 1-894840-38-0

Preamble - Jimmy Wales makes a personal appeal(Wikipedia founder)

On December 31, 2005, in an effort to boost up Wikipedia's end-of-year fundraising drive (rousingly sloganed "Help empower the world with free knowledge!"), the top of every page of Wikipedia started to sport a banner saying: "Please take a moment to read this personal appeal from Wikipedia founder Jimmy Wales." Since this "appeal" is a particulartly revolting piece of demagoguery and puts into relief both the insidious ambitions and the populist lies that fuel the Wikipedia enterprise, it serves as a perfect starting point for our present essay.

A Personal Appeal from Wikipedia Founder Jimmy Wales

Wikipedia is soon to enter our 5th year online, and I want to take a moment to ask you for your help in continuing our mission. Wikipedia is facing new challenges and encountering new opportunities, and both are going to require major funds.

In passing, have you noticed how wherever there is a meeting of the words "mission", "challenges", and "opportunities", it's a safe bet that we are being taken on a gentle journey to the words "major funds"?

Wikipedia is based on a very radical idea, the realization of the dreams most of us have always had for what the Internet can and should become. Thousands of people, all over the world, from all cultures, working together in harmony to freely share clear, factual, unbiased information… a simple and pure desire to make the world a better place.

Oh please. What a shameless crock. Look at any Wikipedia Talk page on any controversial subject, and, instead of "people working together in harmony", you will typically and unsurprisingly see a bunch of mediocre nerds with too much time on their hands and with rather uninformed opinions on too many subjects, bickering among themselves in an attempt to forge an entry that will represent a "consensus" of their uninformed opinions. And on a bad day, you might see among them a displaced person who actually knows something about the topic and has done actual research, being subjected to a hazing because he or she does not want to play along with the "consensus" game. And this is called "making the world a better place"? As for "clear, factual, unbiased information", we have previously described, in great detail, the concerted efforts exerted by Wales' "radical dreamers" to defeat various attempts to place such information in Wikipedia. And any thoughtful examination of any Wikipedia entry concerning a subject of any depth or complexity is likely to reveal, instead, 'information' that is muddled, distorted, factually dubious, often plain ludicrous, and always biased in the direction of mainstream opinion. And what else could be produced by "thousands of people working together"? What else but a "consensual" version of Usenet.

This is a radical strike at the heart of an increasingly shallow, proprietary and anti-intellectual culture. It is a radical strike at the assumption that the Internet has to be a place of hostile debate and flame wars. It is an appeal to the best within all of us.

"Radical strike" our foot. If you want to see "shallow", look at the Wikipedia entry for "Anti-Psychiatry", which mixes together R.D. Laing and Scientology, and references Tom Cruise as a top exponent of the "anti-psychiatry movement". If you want to see "proprietary", look at Wikipedia's recent deal with Answers.com, who will be offering a proprietary 1-click access to Wikipedia (more on that below). And if you want to see "anti-intellectual", just look anywhere in Wikipedia - or, if you don't want to look just anywhere, here is assistant prep-school teacher Theresa Knott - a bright light of the Wikipedia "science squad" and about to become one of the bright lights in the new WikiJunior project - expressing herself on the subject of Aetherometry, which she refuses to read, and on which she has formed an opinion by private consultation with another bright light, Fred Salsbury, who also refuses to read anything about Aetherometry:

More here
http://www.aetherometry.com/Electronic_Publications/Politics_of_Science/Antiwikipedia2/awp2_index.htmlhttp://www.aetherometry.com/Electronic_Publications/Politics_of_Science/Antiwikipedia2/awp2_index.html

Evan
06-04-2010, 09:00 AM
Or this:

From Wikipedia:

WIKIPEDIA MAKES NO GUARANTEE OF VALIDITY

Wikipedia is an online open-content collaborative encyclopedia, that is, a voluntary association of individuals and groups working to develop a common resource of human knowledge. The structure of the project allows anyone with an Internet connection to alter its content. Please be advised that nothing found here has necessarily been reviewed by people with the expertise required to provide you with complete, accurate or reliable information.

That is not to say that you will not find valuable and accurate information in Wikipedia; much of the time you will. However, Wikipedia cannot guarantee the validity of the information found here. The content of any given article may recently have been changed, vandalized or altered by someone whose opinion does not correspond with the state of knowledge in the relevant fields. Note that most other encyclopedias and reference works also have similar disclaimers.

Hupp31
06-04-2010, 10:05 AM
Before we have to call in SpecialOps again to rescue this thread and minimize collateral damage, I want to express my sincere thanks to all who have responded. I've often wondered how much more meaningful my education would have been so many decades ago had more of my instructors presented lessons in the context of everyday problems. Wouldn't it have been nice for the HS geometry classes to get out of the classroom and lay out the various athletic fields - football, soccer, field hockey, both thpes of lacrosse fields, etc.!

I do so appreciate the assistance given here by the assembled masses to a myriad of problems and issues. Additionally, the "friendly banter" is, to me, icing on the cake.

Thanks, Gang.

Phil

Tony Ennis
06-04-2010, 10:13 AM
If you flip a coin 10 time and it comes up heads ten times in a row then what is the chance of it coming up heads on the next flip?

But if the coin is flipped 1000 times and it comes up heads 1000 times in a row, then what is the chance of it coming up heads on the next flip?

That's a little different.

Tony Ennis
06-04-2010, 10:17 AM
I believe wikipedia to be substantively correct for common topics such as the simple type of probability being discussed here.

Oh, and Evan's 'Monty Hall' problem is mind-bending. Work through it if you haven't.

rowbare
06-04-2010, 10:36 AM
But if the coin is flipped 1000 times and it comes up heads 1000 times in a row, then what is the chance of it coming up heads on the next flip?

That's a little different. If you are dealing with a fair coin it is still 50/50. After 1000 flips in a row turning up heads, you can pretty much assume that you are dealing with an unfair coin.

bob

Mcgyver
06-04-2010, 10:37 AM
If you flip a coin 10 time and it comes up heads ten times in a row then what is the chance of it coming up heads on the next flip?

It is still 50/50.

its not 50/50. there's about a 1/1000 chance of flipping 10 heads in a row....presented with that sequence suggests your coin is anything but a random generator and the probability is high that it will be heads next flip unless you slipped it for a tails coin. At that point its time to put the coin away and get out three shells, or go back to photocopy repair :D

dr pepper
06-04-2010, 11:14 AM
If you flipped a coin a 1000 times or a million times and everyone was a head, it doesnt make the slightest difference to the next flip, the chances of getting a head or tail is the same as the first.
But the [I]probability[I] of getting a million heads in a row is extremely unlikely.

Evan was right, we dont think like this as evolution has programmed us not to, our minds think about likelyhood not probability and get the 2 confused.

Mcgyver
06-04-2010, 11:20 AM
If you flipped a coin a 1000 times or a million times and everyone was a head, it doesnt make the slightest difference to the next flip, the chances of getting a head or tail is the same as the first.
But the [I]probability[I] of getting a million heads in a row is extremely unlikely.

the point everyone was making was that your/Evans position assumes the coin toss is a perfect random event generator.....which statistics and probability would say is not the case if in fact you tossed 1000 heads in a row. That 1000 heads in a row is statistically significant proof that coin or toss methodology isn't in fact generating random results so therefor the 1001 flip would not hold 50/50 probability of heads/tails....kind of a Joseph Heller thing :D

Tony Ennis
06-04-2010, 12:18 PM
Yep, the real world is an *ugly* place.

"One of these days in your travels, a guy is going to show you a brand-new deck of cards on which the seal is not yet broken. Then this guy is going to offer to bet you that he can make the jack of spades jump out of this brand-new deck of cards and squirt cider in your ear. But, son, do not accept this bet, because as sure as you stand there, you're going to wind up with an ear full of cider." - Sky Masterson, Guys and Dolls

Evan
06-04-2010, 01:50 PM
ANother interesting probability puzzle is the Birthday Problem.

If you have a room with just 40 people in it what is the probability that any two of them share a birthday?

Of course the answer can be easily found online but the surprising and counterintuitive fact is that the probability is about 90 percent.

As for 1000 flips in a row, that is possible although unlikely. But then, so is winning the lottery on any particular week but almost every week somebody does win it. They had the same chance as anybody else. What really ices the cake is that there are quite a few people that have won twice. There has also been an instance of the same numbers coming up two weeks in a row on a 6-49 type lottery in the US. That really caused a stir but it was proven that the number generator was operating properly.

Unlikely probabilistic events are not impossible.

ckelloug
06-04-2010, 02:34 PM
Mcgyver,

You are right that getting 1000 heads in a row has a vanishingly small probability period equal to 0.5^1000th power. On the scale of geologic time however even events with such a low probability occur occasionally.

In 1000 flips however the chances of getting 10 or 20 heads in a row occurs regularly. It's the fare for dozens of primary and secondary school science fair projects.

Depending on the way which a real coin is flipped, it can be very random or not so random. Probability theory assumes a "Fair Coin": that is one that has exactly .5 probability to land either way. Comparisons of fair coins to real coins aren't really fair as real coins are not perfectly balanced, interact with air currents etc. Replace coin with thermal noise random number generator if you don't want to hypothesize about fair coins and you can reproduce the argument in a very physical albeit abstract way.

Evan,

I'm not going to get into an Evanment with you but I think your hypothesis that everything in the Wikipedia is wrong is utter bollix. In general it has been my observation that the chance of an article being wrong is directly proportional to the popularity of the article.

The technical articles on science and math whose results I have personally verified with software have always been correct. They are often substantially better written than the books I check them against. One example I will give is the example for the bmp file format: Very accurate and one of few places on the web with the complete information. I used this article in writing a decoder for some electron microscope images that were a modified version of BMP.

My results with issues containing controversy such as government policy are mixed with articles showing the bias of the last editor. Take a look at the article on sugar in the wikipedia then look at the history and the editors talk section. Cranks with agendas edit this article all of the time.

I've got a research report I need to be writing so I can't hang out.

Cheers All,
--Cameron

dp
06-04-2010, 03:05 PM
Well, Tiffie, where to start?

They have a strong prejudice for promoting global warming and their climate editor William Connolley finally lost his position over the scandal. It is still impossible to make critical but factual statements regarding what many feel is a disinformation campaign. Wales is a true warmist. A site cannot be considered a resource if it allows even a small part of the content to be skewed by political/agenda motives.

What it is definitely not is is what they claim it is in their About page:

Wikipedia is written collaboratively by largely anonymous Internet volunteers who write without pay.

oldtiffie
06-04-2010, 04:16 PM
Evan,

Well, Tiffie, where to start?

More here
http://www.aetherometry.com/Electronic_Publications/Politics_of_Science/Antiwikipedia2/awp2_index.htmlhttp://www.aetherometry.com/Electronic_Publications/Politics_of_Science/Antiwikipedia2/awp2_index.html

and others of similar nature in support of your post at:

Tiffie,

Wikipedia is filled with trash. You cannot depend on what is posted there. It serves no purpose to post a bunch of links to what anybody on this site can look up if they are so inclined. If you want explanations for math questions try Wolfram Mathworld.

http://mathworld.wolfram.com/

http://en.wikipedia.org/wiki/Probability

http://en.wikipedia.org/wiki/Statistics

http://en.wikipedia.org/wiki/Certainty

http://en.wikipedia.org/wiki/Confidence

http://en.wikipedia.org/wiki/Luck

http://en.wikipedia.org/wiki/Hope

etc.

I accept that the probability of there being errors in Wikipedia is true, but the degree and scope of those errors needs to be considered as well.

Until a statement such as yours is proved or disproved it is only subjective and not objective.

Accepting all of the posts for what they are or maybe in support of there being errors in Wikipedia or not, my post asked you to support your assertion about the specific links that I posted and how wolfram will do it any better.

All that I require is for you to prove on a link-by-link basis how Wikipedia is incorrect and how Wolfram differs and proves Wikipedia incorrect in those links only.

Nothing more and nothing less - conclusively.

In the event that you can and do that, and in the interest of assuring the correctness and integrity of your assertions, I expect that you will be able to and will amend the WP pages contained in the links that I posted so that we are all all the wiser and better informed for it.

Again - that is all that I ask - nothing more and nothing less.

Mcgyver
06-04-2010, 04:50 PM
an Evanment

:D :D too funny. we need a sub forum where Evanment threads can be moved to

Depending on the way which a real coin is flipped, it can be very random or not so random. Probability theory assumes a "Fair Coin": that is one that has exactly .5 probability to land either way.

I completely get probability and that there's no memory and that the toss is assumed to be .5..... just struck a sort of catch 22 funny bone when Evan proposed flipping a coin and getting 10 heads and that the next flip is 50 /50...well its not because its a real world coin and something is up other than probability if there's 10 heads in a row right off the bat....but it has to be because its more than possible to flip 10 heads in a row and so on

In 1000 flips however the chances of getting 10 or 20 heads in a row occurs regularly. It's the fare for dozens of primary and secondary school science fair projects.

having 1000 flips to get 10 in a row is a lot different than stepping and doing it once.....like the birthday Q. because i strangely could find nothing better to do at that precise moment, i made a 10k coin toss in excel and counted the distribution of # of times. everytime you hit F9 you get a different set of data, but it would be improbably not to get at least 10 in a row several times in 10,000 tosses. Graphing it on a log scale is quite linear.....which i guess is to be expected as the nth flip is always 50/50 so there should be half as many 5's than 4's, 6's than 5's etc

# in a row frequency
0 4966
1 2498
2 1271
3 625
4 312
5 157
6 81
7 42
8 28
9 12
10 5
11 2
12 0
13 0
14 0
15 0
16 0
17 0
18 0
19 0
20 0

I've now found something better to do and it involves puttering, the shop and cold one

Evan
06-04-2010, 05:14 PM
I'm not going to get into an Evanment with you but I think your hypothesis that everything in the Wikipedia is wrong is utter bollix.

I didn't say that, did I? I said it's full of trash. That is what is known as hyperbole. It's like saying somebody is full of shlt. The math items are usually correct, but not always. Wrong information abounds and not just on popular items. Even the entry about Williams Lake is riddled with errors. If somebody on the board has decided to look up Williams Lake (probable) they have wildly incorrect information about some fairly important items, such as the racial demographic here. Worse yet the information is credited to Census Canada. The problem is that the person who wrote the article didn't understand statistics.

So, how many other similar articles are equally incorrect? How would you know? Who is going to bother to correct it?

You nor anybody else have any idea what the real quality level is on the Wikipedia site. I am quite sure it is much lower than it appears and worse, much of that incorrect information is very difficult to verify or even correct. Wikipedia is not an encyclopedia. It is an open forum where people may post what they BELIEVE to be true, not what they KNOW to be true. Much of what is written is opinion disguised as fact. The "references" are in many cases unverifiable as they are not available on line.

There is no need and no reason to use Wikipedia as a resource. There are far better resources online that can be trusted to provide accurate information.

Evan
06-04-2010, 05:24 PM
having 1000 flips to get 10 in a row is a lot different than stepping and doing it once.....like the birthday Q. because i strangely could find nothing better to do at that precise moment, i made a 10k coin toss in excel and counted the distribution of # of times. every time you hit F9 you get a different set of data, but it would be improbably not to get at least 10 in a row several times in 10,000 tosses. Graphing it on a log scale is quite linear.

Using a computer to generate so called "random numbers" isn't a valid test. Computers cannot generate random numbers since they are deterministic machines. What they do is generate a pseudo random sequence using a seed value to randomize the start point. Nearly all random number generators will always give the same sequence if given the same seed. Also, the sequence will repeat over and over. How long that takes depends on the particular generator program.

The subject of randomness and the generation of random numbers comprises an entire branch of study in mathematics. It is much harder to generate real random numbers that it may seem. In particular, even if natural analog processes are used to derive random numbers there is almost always some level of bias that can be detected and in some cases be made to compromise a system that uses those numbers.

oldtiffie
06-04-2010, 05:33 PM
Mcgyver,

You are right that getting 1000 heads in a row has a vanishingly small probability period equal to 0.5^1000th power. On the scale of geologic time however even events with such a low probability occur occasionally.

In 1000 flips however the chances of getting 10 or 20 heads in a row occurs regularly. It's the fare for dozens of primary and secondary school science fair projects.

Depending on the way which a real coin is flipped, it can be very random or not so random. Probability theory assumes a "Fair Coin": that is one that has exactly .5 probability to land either way. Comparisons of fair coins to real coins aren't really fair as real coins are not perfectly balanced, interact with air currents etc. Replace coin with thermal noise random number generator if you don't want to hypothesize about fair coins and you can reproduce the argument in a very physical albeit abstract way.

Evan,

I'm not going to get into an Evanment with you but I think your hypothesis that everything in the Wikipedia is wrong is utter bollix. In general it has been my observation that the chance of an article being wrong is directly proportional to the popularity of the article.

The technical articles on science and math whose results I have personally verified with software have always been correct. They are often substantially better written than the books I check them against. One example I will give is the example for the bmp file format: Very accurate and one of few places on the web with the complete information. I used this article in writing a decoder for some electron microscope images that were a modified version of BMP.

My results with issues containing controversy such as government policy are mixed with articles showing the bias of the last editor. Take a look at the article on sugar in the wikipedia then look at the history and the editors talk section. Cranks with agendas edit this article all of the time.

I've got a research report I need to be writing so I can't hang out.

Cheers All,
--Cameron

Cameron.

Good post - many thanks.

"Tossing a coin" or more particularly a pair (two) of coins - "pennies" has been pretty well institutionalised here in OZ with what was pretty well our national (betting) game - "Two Up" - where people bet on the fall of the coins/pennies.

http://en.wikipedia.org/wiki/Two-up

Evan
06-04-2010, 07:11 PM
I have a two up paddle and the pennies to go with it.

Tony Ennis
06-04-2010, 07:48 PM
Using a computer to generate so called "random numbers" isn't a valid test.

It is for what he was talking about. It will tell the gist if not the absolute truth. Most RNGs have a period of the billions, so he's ok for 10k. Scientists use RNGs for all manner of very serious science.

Weston Bye
06-04-2010, 08:19 PM
In the spirit of the Original Post, here is a scenario that any one of us might encounter:

A thug in a parking lot points a gun at you and says "come over here". What do you do? This was posed by a security expert and he outlined his reasoning for advising you to "RUN!"

If you comply, you could end up with the gunmans arm around your neck and the gun to your head. He didn't bother with the odds of survival in that scenario.

However, if you run...
The gunman will either shoot or not shoot - 50/50 - you are at 50% chance of survival.
If he does shoot, the bullet will either hit you or not - 50/50 - you are now at 75% chance of survival.
If the bullet hits you, you will either live or die - 50/50 - you are at 82.5% chance of survival.
An oversimplification, of course, but you get the idea. Seemed like good council to me.

After hearing this, I posed the question to my wife and teen-aged at the time daughters. They all said "comply". NO! NO! NO! ... After regaining my composure, I related the above reasons. They were convinced.

Evan
06-04-2010, 08:32 PM
It is for what he was talking about. It will tell the gist if not the absolute truth. Most RNGs have a period of the billions, so he's ok for 10k. Scientists use RNGs for all manner of very serious science.

Not necessarily. See here:

http://support.microsoft.com/kb/834520/

and here:

For simpler applications, RAND is a good enough simulation of a truly random process. In some situations, however, it is not good enough. This explains why there are third-party alternatives, and why Excel 2003 was kitted out with an upgraded random number generator. Unfortunately, this change introduced a bug that Excel 2003 users should read about here.

The RAND function does not remember its previous output or try to avoid repetition. Any such avoidance would be non-random behaviour.

http://www.iansharpe.com/art_excel_random.php

Tony Ennis
06-04-2010, 08:56 PM
Not always, Evan? Well of course not always.

If you're doing something important, be sure to use a good random number generator.

A thug in a parking lot points a gun at you and says "come over here".

The secondary crime scene is deadly. If you go, you die. Take the bullet in public - someone might call an ambulance.

Evan
06-04-2010, 09:18 PM
Microsoft was notorious for their poor quality random number generators right from the very beginning. Most such random number generators are optimized to be random appearing which means that they will generate numbers without bias in the long term but may have significant short term bias. Some also have "favorite" numbers. This has even plagued mechanical generators. For a long time early in the Lotto 6-49 history in Canada the ball mixing machine had a very distinct preference for certain numbers. They would show up more than twice as often as they should and there was no measurable difference that could explain it.

It can be argued that it is impossible to obtain true random numbers since by the very act of sampling for a value the process that produced it is disturbed. It is a golden rule of Quantum mechanics that the observer always affects what he observes.

Jack Wilson
06-04-2010, 10:14 PM
But if the coin is flipped 1000 times and it comes up heads 1000 times in a row, then what is the chance of it coming up heads on the next flip? That's a little different.

Sure is, clearly that's a double headed coin.

Evan
06-04-2010, 11:24 PM
Thing is, the original post is about a hypothetical situation in which the task is to calculate the pure probabilities. Sure, you can inject all sorts of real world complications but that is not the point of the original post. It also isn't my point about a coin flip. In the realm of probability as it applies to a coin flip it makes no difference how many times it comes up heads. The chance is always 50/50 on every flip.

This also goes to the heart of physics where probability rules all interactions between particles. It also is reflected in thing as diverse as satellite orbits and your heartbeat which are ordered chaotic processes. If you plot your heartbeat timing no two beats have exactly the same interval but the range is always within a max and min (unless you croak). The max and min are surprisingly far apart, on the order of several seconds. The probability of the next heartbeat being very close to the same timing as the previous is very high no matter what that timing is. Most of the time, that is. There are outliers that occur in most healthy people about a dozen times per day. These are usual a result of a sinus arrhythmia cause by stimulation of the sinus nerve in the chest. That produces a "skipped" beat and can happen when you cough or sneeze.

In the macro world we all know that if a coin comes up heads 1000 times in a row there is something fishy. In the world of probabilities it is just another number. It is exactly as likely to occur as any other sequence of heads and tails in 1000 flips of the coin.

philbur
06-05-2010, 04:12 AM
How did I know that Quantum mechanics would show up in this thread?:rolleyes: Here's an old machinist's trick. When the diameter of the part you have just turned is out by a couple of thou just keep re-measuring it until your observations alter the geometry to the size you want. Works every time for me.;)

Phil:)

It is a golden rule of Quantum mechanics that the observer always affects what he observes.

Evan
06-05-2010, 04:40 AM
That works fine for measuring parts but not so well when you are actually making parts. Have you ever actually made any parts?

ptjw7uk
06-05-2010, 05:07 AM
Evan ,
On the coin toss problem how could you tell if the coin was a double headed one or a normal one on the number of heads tossed!
That scenario has always got me pondering about probabilities in the real world!
Peter

psomero
06-05-2010, 07:33 AM
Evan,

unless you can prove otherwise and conclusively that Wikipedia is full of trash (to the exclusion of all other as you say and infer) is pure subjectivity - which you, like anyone else, are quite entitled to have as they are to judge for themselves.

There was a lot of unsubstantiated and non-defined terminology being tossed around, so I decided to post a few links that I think are relevant and that others are able and free to assess for themselves and (to) use and add to - or not - as it suits them.

You, as are any others who choose to do so, are quite entitled to edit or seek to have Wikipedia items edited and revised and judged by you peers.

I look forward to the result of your contributions to Wikipedia.

I have used Wolfram before, and went to the link you posted and (then) to Wolframs Probability and Statistics links at:
http://mathworld.wolfram.com/topics/ProbabilityandStatistics.html

Perhaps, as it seems that you have endorsed Wolfram in that context, that you can show us - or me - where and in what ways Wolfram over-rides and contradicts the Wikipedia links that I posted.

I await your learned discourse which will - or should be able to - prove conclusively that Wikipedia is "filled with trash" - including the topics of probability and statistics which are the theme/s of this thread.

between the time you post a wikipedia link and the time one of us clicks on it, any person can jump on the same article and change it in any way they want, with nothing stopping whatever they decide to add or change from showing up on the internet prior to being subject to scrutiny by anybody.

but don't get me wrong. wikipedia is generally correct due to the fact that there's so many people keeping an eye on things.

the only credible way to use wikipedia as an information resource, though, is to look beyond the wiki page into the references which are cited by it.

don't believe it? see what i did in 30 seconds (then removed, but it still proves my point)

http://www.freeimagehosting.net/image.php?737f46b9e8.jpg

oldtiffie
06-05-2010, 07:50 AM
Paul.

You are quite correct in part as you say and as I have acknowledged previously.

That is both possible and and perhaps probable in the more subjective topics.

Math is hardly subjective but more at or toward the objective.

My only concern, as previously, and still is, that Evan prove that the "math" links that I posted at post # 12 are "rubbish":
http://bbs.homeshopmachinist.net/showpost.php?p=555910&postcount=12

which were and are:

http://en.wikipedia.org/wiki/Probability

http://en.wikipedia.org/wiki/Statistics

http://en.wikipedia.org/wiki/Certainty

http://en.wikipedia.org/wiki/Confidence

http://en.wikipedia.org/wiki/Luck

http://en.wikipedia.org/wiki/Hope

etc.

At post #13:

Tiffie,

Wikipedia is filled with trash. You cannot depend on what is posted there. It serves no purpose to post a bunch of links to what anybody on this site can look up if they are so inclined. If you want explanations for math questions try Wolfram Mathworld.

http://mathworld.wolfram.com/

I suggested that Evan may wish to use wolfram to support and prove his assertion that those Wikipedia "Math" topics and links are "rubbish" and if he wishes, to use any method that he chooses.

I am still awaiting his proof.

psomero
06-05-2010, 08:16 AM
why does evan have to prove that wikipedia may possibly be wrong?

this is a discussion about probability, isn't it?

oldtiffie
06-05-2010, 08:27 AM
Paul.

Evan did not say that Wikipedia may be wrong.

All that I require is that Evan prove his assertion that the WP links I posted - which related to "probabilty" and similar topics - are "rubbish". I assume that he had good reason to support his statement. I'd like to hear/see it.

I am not at all concerned about the rest of WP in this instance.

Evan
06-05-2010, 09:03 AM
All that I require is that Evan prove his assertion that the WP links I posted - which related to "probabilty" and similar topics - are "rubbish". I assume that he had good reason to support his statement. I'd like to hear/see it.

I don't need to prove anything Tiffie. But I will play along.

I selected the link in the middle because it was in the middle. So far this is what I find.

Next is this statement in that article:

This is highlighted in his statement recorded by Plato: "I am wiser than the average man in that I know that I know nothing."

The only references to that supposed quote of Socrates are circular references to the same Wikipedia article (eight of them). No other source in the Google universe contains that particular sequence of words. This makes it highly probable that it is "rubbish".

In that same article is this "information" about an eminent arab philosopher at Nizâmiyya Madrasa religious college :

Al-Ghazali- Islamic theologian
Main article: Al-Ghazali
Al-Ghazali was a professor of philosophy in the 11th century. His book titled The Incoherence of the Philosophers marks a major turn in Islamic epistemology, as Ghazali effectively discovered philosophical skepticism that would not be commonly seen in the West until René Descartes, George Berkeley and David Hume. He described the necessity of proving the validity of reason- independently from reason. He attempted this and failed. The doubt that he introduced to his foundation of knowledge could not be reconciled using philosophy. Taking this very seriously, he resigned from his post at the university, and suffered serious psychosomatic illness. It was not until he became a religious sufi that he found a solution to his philosophical problems, which are based on Islamic religion; this encounter with skepticism led Ghazali to embrace a form of theological occasionalism, or the belief that all causal events and interactions are not the product of material conjunctions but rather the immediate and present will of God.

However, at Stanford University we find this explanation:
http://plato.stanford.edu/entries/al-ghazali/

I prefer to trust Stanford over an unsupported entry in the Wikipedia. The Stanford article gives an extensive list of sources and resources, too long to post here.

There is more but that is plenty enough to prove my point.

Tony Ennis
06-05-2010, 09:32 AM
Words like "rubbish" are ill defined in this context. In the context of machining, one man's 'rubbish' is another man's 'cosmetic flaw.'

If I were using wikipedia for important research I'd use it to learn the gist of the topic, which I am positive it would be good for. I'd use the references to get more trustworthy information. Or what I've learned to find other research materials.

So is a source you can't really trust rubbish? Maybe. Is a source that is generally good enough to allow one to have a discussion about the topic rubbish? Maybe not.

Richard-TX
06-05-2010, 11:27 AM
Wikipedia isn't horrible. It is just another bit of information derived from a different source and as such, data within it is questionable. The same thing can be said about textbooks and other traditional sources of data. Even pure numbers stored on a computer is questionable. When someone makes a claim, and it doesn't seem right, I attempt to verify it with some credible sources or by experiment if I am so inclined.

Some years ago, there was a "did you know" document that was floating around the internet. It was claimed in that document that the human eye does not change size from birth to adulthood. That bit of misinformation is now so prevalent that it is has almost taken on a life of it's own.

When researching facts, it is better to try to prove a fact wrong than to prove it right. The number of positive or negative hits for a fact doesn't make it true either.

"A lie told often enough becomes the truth" is part of the problem and if one does proper root cause analysis, the problem lies within humans themselves. Humans are notoriously bad in maintaining accuracy. There is more than enough evidence to support that assertion.

Evan
06-05-2010, 12:00 PM
The problem with Wikipedia is that it calls itself an Encyclopedia when in fact it is a forum. There is no requirement that anything that is posted be the product of appropriate research. There is quite a difference between something being incorrect in a text book or reference and something being incorrect in Wikipedia. Textbook mistakes are either inadvertant errors or they usually represent the concensus of learned opinion at the time which may have been mistaken. Wikipedia errors are often the result of vandalism, ingorance and/or the posting of opinion as fact. These types of errrors are all in addition to the usual errors that one might find in a text and are far more common as well.

There is also the problem illustrated by the link I checked out. While it bears a disclaimer about the lack of references it still stands with no attempt to verify the veracity of the article.

ckelloug
06-05-2010, 12:13 PM
Evan is right that Microsoft random number quality has been at issue in the past.

On the other hand, computer generated pseudo-random numbers using a competently deigned algorithm are used in many scientific fields and they work well.

Modern U.S. nuclear weapons are designed using computer generated pseudo-random numbers and they work just fine. The software package is called MCNP and I worked on it myself at Los Alamos National Laboratories. The name stands for Monte Carlo N Particles. This software is used for weapons design, reactor shielding design, and medical dosage computations. I ported it to Linux for a brain cancer treatment called Boron Neutron Capture Therapy.

*NERD Appendix*

Simply calling the rand() routine from the C standard library is not a great way to get random numbers as it is seeded with the same value every time and will give you the same sequence each time. For better results, one must seed it with srand(). There are better linear feedback random number generators in the libraries on linux and other OS's for more scientific applications needing more randomness but not all applications require near-prefect randomness to be quite successful.

Truly random numbers can be generated by measuring a physical phenomenon such as thermal noise which is truly random and quantizing it.

Evan
06-05-2010, 01:13 PM
While values generated by a physical process may be considered truly random that doesn't preclude those values from exhibiting a bias. Randomness and bias are not mutually exclusive but for most random number based applications a bias is not acceptable.

Shot noise in particular usually has a 1/f spectrum. That means the bias will vary with the sample period. Bias is also present with beta radioactive decay which is another source of natural random numbers. Also, thermal noise will be quantized which means that for certain short sample periods certain values will be excluded.

Here is a description by John Walker, the co-creator of AutoCad, of how to extract random numbers from radioactive decay. He explains a couple of the main complications and also offers free random number sets from his site that are guaranteed never to be offered to anyone else.

To create each random bit, we wait until the first count occurs, then measure the time, T1, until the next. We then wait for a second pair of pulses and measure the interval T2 between them, yielding a pair of durations. If they're the same, we throw away the measurement and try again. Otherwise if T1 is less than T2 we emit a zero bit; if T1 is greater than T2, a one bit. In practice, to avoid any residual bias resulting from non-random systematic errors in the apparatus or measuring process consistently favouring one state, the sense of the comparison between T1 and T2 is reversed for consecutive bits.

http://www.fourmilab.ch/hotbits/how3.html

Incidentally, he has quite of bit of free software on his site that is worth looking at.

dp
06-05-2010, 01:27 PM
Quote:

This is highlighted in his statement recorded by Plato: "I am wiser than the average man in that I know that I know nothing."

The only references to that supposed quote of Socrates are circular references to the same Wikipedia article (eight of them). No other source in the Google universe contains that particular sequence of words. This makes it highly probable that it is "rubbish".

This is more a problem of Google fu and common human error than something being rubbish. As a bit of a scholar I often find that searching for a fully qualified quote will end in failure, but if you break it down into plausible sections you will find much.

If you Google for "I am wiser than the average man" (sans quotes) you will find all manner of similar versions, and perhaps even what old Plato actually said about Socrates, assuming you speak old Greek.

A translated quote is impossible to quote perfectly because so much depends on the translation. The quote given though, is mangled English and so deserves to be replaced on Wikipedia with a version that is not mangled. Aside from that it appears to be traceable to Socrates.

That said, Wikipedia is by policy a dumping ground for any wank trying to preserve history as it exists in their minds, and there is a lot of sanctioned BS that goes on there by the "editors".

Edited my own mangling ;)

philbur
06-05-2010, 02:15 PM
If you read my post more carefully you should be able to deduce the answer to your question.

Phil:)

That works fine for measuring parts but not so well when you are actually making parts. Have you ever actually made any parts?

dp
06-05-2010, 02:42 PM
Truly random numbers can be generated by measuring a physical phenomenon such as thermal noise which is truly random and quantizing it.

I like the way openssl software builds an entropy pool using a number of physical artifacts: log files, timing keystrokes at the keyboard, etc. If nothing else the seed is reasonably expected to be unique for that system over a reasonable lifetime.

Global entropy pools can be created using screen savers similar to what SETI@home was doing. Seeds of various sizes can then be stored in a central database and tossed out when issued.

Alistair Hosie
06-05-2010, 03:06 PM
Evan you would have much more fun with a goat than a car so why bother?if it turns out to be ugly then you could always turn it into a submarine or a washing machine anyway. Alistair

Evan
06-05-2010, 03:07 PM
This is more a problem of Google fu and common human error than something being rubbish. As a bit of a scholar I often find that searching for a fully qualified quote will end in failure, but if you break it down into plausible sections you will find much.

What it tells me is that the poster of the article mangled it himself and didn't care enough to be more accurate.

oldtiffie
06-05-2010, 07:48 PM
There is a lot of talking about and perhaps evading my direct request.

Bluster and filibustering are just trying to obscure or evade the issue and not (to) address it.

All that I require is for Evan to use one of his numerous credible sources and resources to show that the substance of the links I referred to are "rubbish".

Nothing more and nothing less.

Evan may have used "rubbish" as a throw-away line but in the context that he made it and given that he has neither retracted his assertion nor said that he did not like it on personal rather than technical or mathematical grounds, I have to assume that he meant what he said then and still does.

My post (#11) that we refer to is:

http://en.wikipedia.org/wiki/Probability

http://en.wikipedia.org/wiki/Statistics

http://en.wikipedia.org/wiki/Certainty

http://en.wikipedia.org/wiki/Confidence

http://en.wikipedia.org/wiki/Luck

http://en.wikipedia.org/wiki/Hope

etc.

Evan's reply at post #13 was/is:

Tiffie,

Wikipedia is filled with trash. You cannot depend on what is posted there. It serves no purpose to post a bunch of links to what anybody on this site can look up if they are so inclined. If you want explanations for math questions try Wolfram Mathworld.

http://mathworld.wolfram.com/

My response at post #14 was and is:

Evan,

unless you can prove otherwise and conclusively that Wikipedia is full of trash (to the exclusion of all other as you say and infer) is pure subjectivity - which you, like anyone else, are quite entitled to have as they are to judge for themselves.

There was a lot of unsubstantiated and non-defined terminology being tossed around, so I decided to post a few links that I think are relevant and that others are able and free to assess for themselves and (to) use and add to - or not - as it suits them.

You, as are any others who choose to do so, are quite entitled to edit or seek to have Wikipedia items edited and revised and judged by you peers.

I look forward to the result of your contributions to Wikipedia.

I have used Wolfram before, and went to the link you posted and (then) to Wolframs Probability and Statistics links at:
http://mathworld.wolfram.com/topics/ProbabilityandStatistics.html

Perhaps, as it seems that you have endorsed Wolfram in that context, that you can show us - or me - where and in what ways Wolfram over-rides and contradicts the Wikipedia links that I posted.

I await your learned discourse which will - or should be able to - prove conclusively that Wikipedia is "filled with trash" - including the topics of probability and statistics which are the theme/s of this thread.

The nub of the issue is in those three posts.

I do not doubt in any way that there are some real and potential issues of accuracy in Wikipedia but there is always the option/s of pursuing the issue in the references appended to the main article/s. WP seems to me to be quite adequate in most ways for my purposes, but I have the option of looking else-where for confirmation or rebuttal - if I think it necessary and if I chose to.

I just want to know where and in way those links are wrong ie "rubbish" - or not.

If they are "rubbish" - show me.

If they are not "rubbish" - tell me.

No more and no less.

dp
06-05-2010, 08:01 PM
Tiffie - many of the Wikipedia topics have very active discussion links on the page. The real dark underbelly of Wikipedia is found by reading these discussions. Not every topic is going to be controversial or have an active discussion page, but you need find only a few that are very active to get a good feel for what the political/editorial leaning is there.

oldtiffie
06-05-2010, 08:54 PM
Thanks Dennis.

I have been down that dark and dingy WP road a couple of times as a reader/observer and NOT as a participant so I feel that I have some sort of "feel"??? for those "discussions". They seem to aspire or do equate to learned articles in learned professional journals for discussion etc. with learned peers. I certainly cannot aspire to such lofty and ethereal circles.

I really don't have - or perhaps I do have - a hidden agenda here.

My post (12) with the link in it was logged at: 06-04-2010, 09:24 AM

Evan's refutation (13) of those links was logged at: 06-04-2010, 11:39 AM

a gap of ~2 hours.

My reply (14) to Evan was logged at: 06-04-2010, 12:09 PM

a gap of ~ 1/2 hour

Evan had his answer/response posted in 2 hours so I guess he used his resources to develop and back up his seemingly quick response.

If the assumption implicit in that is correct, then Evan should have no trouble answering my request to substantiate his assertion that those links - and only those links - to the exclusion of any and all others - are "rubbish".

I am quite prepared to wait patiently and to respond as, how, when and if necessary.

I am not and don't want to give the impression that I am or that I regard myself as any sort of "Math Guru". I am just an interested party.
[End edit]

Evan
06-05-2010, 09:02 PM
I just want to know where and in way those links are wrong ie "rubbish" - or not.

I have already given an example. It was the very first item I chose and is prefaced with a disclaimer of unverified content. I didn't make specific reference to the particular links you posted. You constantly post links as the only or majority content of your postings, nearly always to Wikipedia. It serves no useful purpose. If you want to clarify the meaning of something you could at least post a sentence as a quote with attribution. I never follow links to Wikipedia and frequently don't to other sites as it is much too time consuming.

Better yet, find information at authoritative sources where there is at least a fair assurance it will be correct. Wolfram is such a resource for mathematics. I don't even use Google all that much because I know or have bookmarked a wide variety of direct information resources. I also have an extensive library both in paper and electronic format that is quite comprehensive. I have read the books in my library, they are not for show. That room is off limits to everybody except myself and my wife.

You cannot discover anything by looking at the timing of my responses. I have many other things to do with my time and on some days I don't check in here except at night.

oldtiffie
06-05-2010, 09:17 PM
Evan,

I take your point that I should have included some explanatory text, but in the context at the time I thought it was not necessary as I thought is was self-evident.

Am I correct in reading in(to?) your response that you either cannot or will not directly answer my direct request regarding the correctness or otherwise of the specific links that I referred to?

In short:
- are they "rubbish" or not; and
- if so, where and why and in what way/s are they and how do you verify it?

Evan
06-05-2010, 09:32 PM
I am not going to look up the other links. I have better things to do. I have made my point.

dp
06-05-2010, 09:38 PM
This reminds me of a story...

oldtiffie
06-05-2010, 10:15 PM
I am not going to look up the other links. I have better things to do. I have made my point.

You have indeed Evan.

oldtiffie
06-05-2010, 10:50 PM
This reminds me of a story...