100000 women

A funny example from probability calculus:

Consider a set of 100000 women, all of which are regularly taking the birth control pill (probability of success: 99.99%). Furthermore, they all do a pregnancy test (probability of success: 99.99%).

What is the probability that given a positive test result, this actually implies a pregnancy?


Here's the calculation:

100000 * 0.0001 = 10 women will get pregnant despite taking the pill and hence get a positive test result
(the pill fails with probability 0.01%).

100000 * 0.0001 = 10 women will get a positive test result, although they are not pregnant
(the test fails with probability 0.01%)


So, out of 20 positive test results, only 10 women are actually pregnant. Thus, the probability that a positive test result implies a pregnancy is 50%.

What does that tell you?

Greets,
Philip

Yeah, just like the chances of winning the lottery is 50%: You either win, or you don't!

--
Mats

[Jimmy the Hand]I'd rather be lucky than good any day.[/Jimmy the Hand]

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What does that tell you?

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Do more pregnancy tests! The more the better, just to make sure. Where do I get mine?

I tried to do a pregancy test once. What does the color brown mean?






okay, no taste, sorry.

Is the probability of success the probability of pregnancy or the probability of getting the right result?

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So, out of 20 positive test results, only 10 women are actually pregnant. Thus, the probability that a positive test result implies a pregnancy is 50%.

What does that tell you?

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There's no point in having a test whose error rate is the same as the rate of actual positive results.

Nope. That is only when a birth control pill is used. It only means that the same number of women get the wrong results as the number of women being pregnant. But yes, anyone could be pregnant with a fifty-fifty chance.

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Nope. That is only when a birth control pill is used.

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Yes, that's the premise.
To put it in clearer points, there's not much point in doing a 99.99% certainty pregnancy test if you're also using a 99.99% contraceptive, because a positive result only gives you 50% certainty that you're actually pregnant, instead of the advertised 99.99%.

Of course, that's assuming that pregancy rate without contraceptive is 100%, which it isn't.

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Originally Posted by CornedBee

Yes, that's the premise.
To put it in clearer points, there's not much point in doing a 99.99% certainty pregnancy test if you're also using a 99.99% contraceptive, because a positive result only gives you 50% certainty that you're actually pregnant, instead of the advertised 99.99%.

Of course, that's assuming that pregancy rate without contraceptive is 100%, which it isn't.

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The entire test begins with the premise that both of the tests are 99.99% effective

50% of the .01% of the people who used the pregnancy test will be pregnant

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Originally Posted by Snafuist

Thus, the probability that a positive test result implies a pregnancy is 50%.

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This is almost a non-sequiter. Who are you trying to fool, your cat?

Here's something I read the other day, I hope you aren't offended Snafuist:

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This is like the joke about the German proclivity toward double abstractions; a German authority on English literature declares, "Hamlet was not written by Shakespeare; it was merely written by a man named Shakespeare." In English the distinction is verbal and without meaning, although the German language will express the difference (which accounts for some of the strange features of the German mind).

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I believe this, although I don't speak German (but my father is Danish born and these languages are almost identical AFAIK). Probably that was from studying a lot of Husserl and Heidegger. A disproportionate percentage of the best continental philosophers were German, I assume because the language lends itself to well to that. "Original flavour" in Anglo philosophy tends to be either whimsically banal, or stale and reductive ("analytic"). There are some great English deconstructionists/post-modernists, but really that is French in origin.

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This is like the joke about the German proclivity toward double abstractions; a German authority on English literature declares, "Hamlet was not written by Shakespeare; it was merely written by a man named Shakespeare." In English the distinction is verbal and without meaning, although the German language will express the difference (which accounts for some of the strange features of the German mind).

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Huh? The semantics of the equivalent German sentences are absolutely identical with the English version. I have no idea what this guy is trying to imply, but unless there's something about the English mind I don't understand, there's nothing to it.

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Originally Posted by MK27

This is almost a non-sequiter. Who are you trying to fool, your cat?

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It's perfectly valid. The surprising answer is a result of the tricky question: it selects a very small subset of the original 100000 women, namely those 20 with a positive test result, and then asks for a certain property among those.

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Here's something I read the other day, I hope you aren't offended Snafuist:

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It's extremely hard to offend me, and you certainly need more practice.

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I believe this, although I don't speak German (but my father is Danish born and these languages are almost identical AFAIK).

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German and Danish share several properties, but Danish is much more similar to other Scandinavian languages (Swedish, Norwegian). While a typical German can partly understand written Danish (relying on guessing and context), the language is indistinguishable from nonsense babble in its spoken form.

An example:
The Danish language (English)
Die dänische Sprache (German)
Det danske sprog (Danish)

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This is like the joke about the German proclivity toward double abstractions; a German authority on English literature declares, "Hamlet was not written by Shakespeare; it was merely written by a man named Shakespeare." In English the distinction is verbal and without meaning, although the German language will express the difference (which accounts for some of the strange features of the German mind).

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I'm certainly not denying that the German mind tends to be extraordinarily complicated, but I think the sentence "Hamlet was not written by Shakespeare; it was merely written by a man named Shakespeare" has the same meaning in both German and English. Every German would immediately interpret the literal translation of this sentence as "Hamlet was not written by this famous Shakespeare guy; it was merely written by someone else who just happens to have the same name."

Does the sentence have a different meaning for English native speakers?

I'd be interested to hear which "German authority on English literature" you're referring to. The cited sentence is a joke, and most "German authorities" refrain from making jokes in their publications.

Greets,
Philip

PS:

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Originally Posted by CornedBee

"There is not now, nor has there ever been, nor will there ever be, any programming language in which it is the least bit difficult to write bad code."
- Flon's Law

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Snafuist's Commentary:
But Malbolge makes a pretty tough attempt.

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Originally Posted by MK27

(but my father is Danish born and these languages are almost identical AFAIK).

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...no

English and Danish have more in common than German and Danish....Alot more in common actually.

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Originally Posted by Snafuist

It's perfectly valid. The surprising answer is a result of the tricky question: it selects a very small subset of the original 100000 women, namely those 20 with a positive test result, and then asks for a certain property among those.

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actually, the 20 with an incorrect result
50% were pregnant and receved a negitive result
50% were not and received a positive result

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Originally Posted by Snafuist

"Hamlet was not written by this famous Shakespeare guy; it was merely written by someone else who just happens to have the same name."

Does the sentence have a different meaning for English native speakers?

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no

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Originally Posted by ಠ_ಠ

actually, the 20 with an incorrect result
50% were pregnant and receved a negitive result
50% were not and received a positive result

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No, the 20 with a positive result:
50% are pregnant and hence get a positive result
50% are not pregnant, but get an incorrect and hence positive result

Greets,
Philip

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Originally Posted by Snafuist

No, the 20 with a positive result:
50% are pregnant and hence get a positive result
50% are not pregnant, but get an incorrect and hence positive result

Greets,
Philip

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so no pregnant women receive negative results?

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Originally Posted by ಠ_ಠ

so no pregnant women receive negative results?

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Probably not.

The test shows the correct result in 99.99% of all cases. There are 10 pregnant women. 99.99% of 10 pregnant women is more or less 10 pregnant women.

Greets,
Philip

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Originally Posted by Snafuist

I'm certainly not denying that the German mind tends to be extraordinarily complicated, but I think the sentence "Hamlet was not written by Shakespeare; it was merely written by a man named Shakespeare" has the same meaning in both German and English. Every German would immediately interpret the literal translation of this sentence as "Hamlet was not written by this famous Shakespeare guy; it was merely written by someone else who just happens to have the same name."

I'd be interested to hear which "German authority on English literature" you're referring to.

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The "German Authority" is fictional AFAIK since the context of the quote is from a piece of fiction; it just rang bells vis. my formal study of (German) philosophy (which I like, esp Nietzsche).

So perhaps the example is bad and was intended for anglophones familiar with such, as is actually not an uncommon technique in 20th century English literature: because the lineage Husserl -> (Heidegger*) -> Derrida was *the* predominant stream of 20th century western philosophy, and 20th century English writers were aware of it. It is probably a pun on the idea: one acquired this "awareness" there, so the reader may or may not get the joke. The awareness being a nuanced slant in English but perhaps a more concrete distinction in German -- "German" being, metaphorically or mythologically, a language like "Japanese" in (common, later, 20th century) English parlance: something frightening -- technically superior but alien. I still believe this is *slightly* more than metaphorical (but I also believe English is the most modern, and probably most complex, language in the world; the "German" or "Japanese" person is really a mirror for the implication: who wants to be the dominant alien?).

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Does the sentence have a different meaning for English native speakers?

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It could, but most people would disagree about what that was. So since the source is *literary*, I guess the point is a distinction between the naive (English/literal) type person and the sophisticate (German/interpretive) type person that I just mentioned.

Going back to my comment about the OP being a near non-sequiter: it is. In this case the naive Englishman would cling to the paradigm of "probability calculus" despite the ridiculousness of the conclusion this forces upon him, whereas the sophisticate German would not be so bound, but unable to explain to the Englishman why he is a fool -- because the Englishman does not have the (linguistic) capacity to understand his naivete.

w/r/t German, Danish, et. al., my dad could communicate in Danish, German, Swedish, Norwegian to some extent because of the similarities (having witnessed this), but I cannot see such a possibility English -> German. If you watch Danish television (often German with Danish subtitles), it is almost funny how much the the spoken German "sounds like" the Danish subtitles. But I do not speak either language, so maybe that is my naivete ;) after all, the subtitles must have been there for a reason.

* KICKS ASS

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Originally Posted by CornedBee

Of course, that's assuming that pregancy rate without contraceptive is 100%, which it isn't.

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It is when I'm 'The Impregnator' :)

I'll be back.

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Originally Posted by abachler

It is when I'm 'The Impregnator' :)

I'll be back.

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Well. Governers of California rejoice friends, here is your evidence.

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Originally Posted by MK27

"German" being*, metaphorically or mythologically, a language like "Japanese" in (common, later, 20th century) English parlance: something frightening -- technically superior but alien.

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*pretty much Austria.

We covered a similar problem like this at school. I believe the idea was to come across that the test needs to be run multiple times for best accuracy. Somehow this was related to mobile robotics, and how sensor inputs ideally will take multiple readings for the best accuracy.

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Originally Posted by MK27

The awareness being a nuanced slant in English but perhaps a more concrete distinction in German

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No, it's a nuanced slant in German as well. But the German mind is arguably more prone to spotting those nuances: in German, it's hard to formulate simple statements and not sound like a moron.

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"German" being, metaphorically or mythologically, a language like "Japanese" in (common, later, 20th century) English parlance: something frightening -- technically superior but alien.

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I can easily comprehend that German must seem frightening, and it's probably very hard for non-native speakers to get used to the language. In my opinion, this is mostly due to German being a synthetic language (i.e. words reflect their grammatical role within a sentence by using morphemes). The correct sub-category is "flektierende Sprache", which is probably "flecting language" in English.

Here's an example:

Hans gibt seiner Schwester 10 Piepen für deren Eltern Geburtstagsgeschenk
(Hans pays his sister 10 bucks for their parents' birthday present)

Hans gibt seiner Schwester für deren Eltern Geburtstagsgeschenk 10 Piepen
(Hans pays his sister for their parents' birthday present 10 bucks)

Hans gibt für deren Eltern Geburtstagsgeschenk seiner Schwester 10 Piepen
(Hans pays for their parents' birthday present his sister 10 bucks)

Seiner Schwester gibt Hans 10 Piepen für deren Eltern Geburtstagsgeschenk
(His sister pays Hans 10 bucks for their parents' birthday present)

Seiner Schwester gibt Hans für deren Eltern Geburtstagsgeschenk 10 Piepen
(His sister pays Hans for their parents' birthday present 10 bucks)

10 Piepen gibt Hans seiner Schwester für deren Eltern Geburtstagsgeschenk
(10 bucks pays Hans his sister for their parents' birthday present)

10 Piepen gibt Hans für deren Eltern Geburtstagsgeschenk seiner Schwester
(10 bucks pays Hans for their parents' birthday present his sister)

10 Piepen für deren Eltern Geburtstagsgeschenk gibt Hans seiner Schwester
(10 bucks for their parents' birthday present pays Hans his sister)

Für deren Eltern Geburtstagsgeschenk gibt Hans seiner Schwester 10 Piepen
(For their parents' birthday present pays Hans his sister 10 bucks)


In German, all these sentences have the exact same meaning. In English, only the first one actually has a meaning at all. Hence, it doesn't suffice to recognize the meaning of a German word, one must also determine its gender, grammatical number and grammatical case (for nouns) and tense, person, gender, mood, grammatical aspect and lexical aspect (for verbs). A lot of these combinations lead to slightly different words (which is good, because otherwise one also has to consider the context). This must be a nightmare for English native speakers.

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but I also believe English is the most modern, and probably most complex, language in the world

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Of all the languages I know (German, English (which I can speak more or less fluently), and French, Latin (which I can read and understand with the help of a dictionary)), English is by far the easiest language, both to understand and to write. What makes you believe that it's "probably the most complex language in the world"? Most German native speakers would consider such a statement to be outright ridiculous.

Occasionally, I like to formulate my thoughts in English, especially when I'm thinking about algorithms or other topics related to CS. That's because in English, it's simply not possible to construct complicated sentences. In German, you can easily write a whole book consisting of only one sentence.

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because the Englishman does not have the (linguistic) capacity to understand his naivete.

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In Germany, it's a common belief that all North-Americans are fat and stupid, but this is probably not what you intended to say ;-)

Have you heard about the Sapir-Whorf Hypothesis?

Greets,
Philip

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Originally Posted by Snafuist

Have you heard about the Sapir-Whorf Hypothesis?

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I'll go as high as $30 US

So Thanks for that Snafuist but I think you meant Tapir-Warf Hypothesis:

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Originally Posted by Snafuist

Probably not.

The test shows the correct result in 99.99% of all cases. There are 10 pregnant women. 99.99% of 10 pregnant women is more or less 10 pregnant women.

Greets,
Philip

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there are 1000 pregnant women (given abachler is the father (lots of child support lol) )

there are 1000 incorrect pregnancy tests

there are 10 pregnant women who had a negative pregnancy test result

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Originally Posted by ಠ_ಠ

there are 10 pregnant women who had a negative pregnancy test result

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Apparently the "B" is 10 of 10 after is somewhat sick, U no I love her anyways and get stupid, odddd bless

[later] I have decided to give up drinking ;)

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Originally Posted by mk27

apparently the "b" is 10 of 10 after is somewhat sick, u no i love her anyways and get stupid, odddd bless

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what the ........ are you saying?

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Originally Posted by neandrake

We covered a similar problem like this at school. I believe the idea was to come across that the test needs to be run multiple times for best accuracy. Somehow this was related to mobile robotics, and how sensor inputs ideally will take multiple readings for the best accuracy.

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Typically this is done in machine vision, as there is quite significant levels of artifacts in a single captured image, but if you average even a few images together (as few as 2-3), the anomolies mostly go away. This of course can lead to new types of anomolies appearing, mostly on cheap low end webcams though, where you can actually see the boundaries of the individual cmos arrays. CCD doesn't have this problem generaly because CCD cameras use a monolithic imaging chip.

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w/r/t German, Danish, et. al., my dad could communicate in Danish, German, Swedish, Norwegian to some extent because of the similarities (having witnessed this)

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Yes, Danish, Swedish and Norwegian are all very similar, all danes understand all swedes and norwegians, and ofcourse the other way around.

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If you watch Danish television (often German with Danish subtitles),

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95% of Danish TV is either in Danish, or in English with subtitles, i have a hard time remembering last time i watched German TV on a Danish TV station.

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it is almost funny how much the the spoken German "sounds like" the Danish subtitles. But I do not speak either language, so maybe that is my naivete after all, the subtitles must have been there for a reason.

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I am not a linguist, (nor am i an expert in Danish TV, or well, not professionally atleast :P), but i have been taking German classes for the last 6 years of my life, and i still have trouble understanding it, so do many of my classmates.
German does not come naturally to Danes, unless they live very close to the border.

Edit:

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Originally Posted by snafuist

Occasionally, I like to formulate my thoughts in English, especially when I'm thinking about algorithms or other topics related to CS

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Funny, i do the exact same thing! And here i was thinking i was the only one, yay, i'm normal!

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Originally Posted by Neo1

95% of Danish TV is either in Danish, or in English with subtitles, i have a hard time remembering last time i watched German TV on a Danish TV station.

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I had that experience when I was 16, so 20 years ago. Denmark's a nice place; more recently when I was there I didn't watch any TV, except for a video tape of the last police raid on "Freetown Christiania" from before it was declared a historic site and protected by the government*. I lived in Christiania for a few months, it was one of the most amazing places I have ever been, and I've travelled a fair bit. Sadly, it would never, never, be allowed to exist in the USA.

*I just read the wikipedia article and it sounds like the government changed and has now decided to ruin the place. Too bad...I had been looking forward to going back one day. Very bad, from the sounds of it, in fact.

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Originally Posted by MK27

*I just read the wikipedia article and it sounds like the government changed and has now decided to ruin the place.

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Yesterday (May 26), the court which is responsible for this area (Østre Landsret) decided the evacuation of Christiania.

Makes me sad and angry.

Greets,
Philip

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Originally Posted by MK27

I had that experience when I was 16, so 20 years ago. Denmark's a nice place; more recently when I was there I didn't watch any TV, except for a video tape of the last police raid on "Freetown Christiania" from before it was declared a historic site and protected by the government*. I lived in Christiania for a few months, it was one of the most amazing places I have ever been, and I've travelled a fair bit. Sadly, it would never, never, be allowed to exist in the USA.

*I just read the wikipedia article and it sounds like the government changed and has now decided to ruin the place. Too bad...I had been looking forward to going back one day. Very bad, from the sounds of it, in fact.

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Christania is an amazing place, if you like the atmosphere and spirit of the freetown, you should try the Roskilde Festival at some point, more of the same :)

As for the court order, it has yet to go through the supreme court, and the lawyer team representing Christania thinks they have a good case. More on that subject here.

This entire situation is a product of 8 years with a liberal government and the extremist nationalist people's party, it's very sad!

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Originally Posted by Neo1

This entire situation is a product of 8 years with a liberal government and the extremist nationalist people's party, it's very sad!

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Wow -- evacuation! I've never really felt the desire to pick up arms before and join a foreign struggle, but this almost would be the case. Of course that is not the answer. I imagine the people that have lived there for decades and raised families are not happy (for those that don't know, Christiania was an 18th or 19th century military barracks abandoned in the late 60's). They even built playgrounds. It's in the middle of Copenhagen and they don't allow cars inside the walls which still surround it. Very alternative. Etc, etc. Because it was built for the military, no one was able to cut off the utilities.

This is not in the news here at all. Maybe it will be on the BBC in a few hours. Why do you think the people of Denmark, who were "nearly socialists" for so long*, suddenly in the past ten years decided they wanted such a "bad" government?

*that is actually the reason my father emmigrated; he didn't want to pay taxes and felt the business climate would be better for entrepreneur types in North America, so he came here to make money. Which he did. But as an irony, his brother, who is also a mechanical engineer, stayed in Denmark and made even more money.

Look guys, I spoke german and english in the home until I was 5 years old, this haughty attitude that most germans have about how their language is spoken is an entirely modern eurotrash phenomenon. Remember that most of the educated affluent germans left germany prior to 1939 due to the failing economy, what was left was, well, lets not be overly prejudicial in our analysis, the ones that couldnt or wouldnt leave.

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Originally Posted by MK27

This is not in the news here at all. Maybe it will be on the BBC in a few hours. Why do you think the people of Denmark, who were "nearly socialists" for so long*, suddenly in the past ten years decided they wanted such a "bad" government?

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People got rich, didn't want to share, i guess? If you are in the top income bracket, which nearly 1/3rd of the country is, you get to pay 62% taxes, back before the liberal government, that number was a bit higher, guess the voters got fed up with it. That's my take on the situation at least, i'm not liberal so i wouldn't really know.

Problem is, with a liberal government, places like Christania, and Ungdomshuset will eventually be shut down, as it goes directly against the liberal ideology.

To be fair, the liberal government got the unemployment rate down, to unprecedented levels. Luckily, their politics will not be beneficial for Denmark in the current financial crisis, which hopefully will get the 'commies' back on the throne (Or so the economical and political experts say, at least)

So, your chance to do something wrong are 10.000 / 20 = 1 to 500.

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Originally Posted by Neo1

Problem is, with a liberal government, places like Christania, and Ungdomshuset will eventually be shut down, as it goes directly against the liberal ideology.

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That Ungdomshuset story is pretty harsh, esp. since it was evangelical right-wing Christians that bought it so they could tear the place down and sell the real estate! There's some familiar Christian meaness and hatred for you!

The significance of "liberalism" in Europe is I believe somewhat the opposite of it what it is here.

There has been no mention of this on the BBC world service. Instead, they are talking about all the sad stupid asses that lost money with Bernie Madoff. I would bet money that a lot of those people would also be the kind of people who would vote against the squatters of Christiania, and drive them out of their homes. But they are now crying for sympathy because "they have unfairly lost their life savings" thanks to some other money-grubber outwitting them. Haha.