100000 women

This is a discussion on 100000 women within the A Brief History of Cprogramming.com forums, part of the Community Boards category; A funny example from probability calculus: Consider a set of 100000 women, all of which are regularly taking the birth ...

  1. #1
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    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
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    Yeah, just like the chances of winning the lottery is 50%: You either win, or you don't!

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    The superhaterodyne twomers's Avatar
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    [Jimmy the Hand]I'd rather be lucky than good any day.[/Jimmy the Hand]

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    Dr Dipshi++ mike_g's Avatar
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    What does that tell you?
    Do more pregnancy tests! The more the better, just to make sure. Where do I get mine?

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






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

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    Cat without Hat CornedBee's Avatar
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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?
    There's no point in having a test whose error rate is the same as the rate of actual positive results.
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    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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    Cat without Hat CornedBee's Avatar
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    Nope. That is only when a birth control pill is used.
    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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    Quote Originally Posted by CornedBee View Post
    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.
    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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    spurious conceit MK27's Avatar
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    Quote Originally Posted by Snafuist View Post
    Thus, the probability that a positive test result implies a pregnancy is 50%.
    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:
    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).
    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.
    Last edited by MK27; 05-25-2009 at 01:36 PM.
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  12. #12
    Cat without Hat CornedBee's Avatar
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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).
    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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    Quote Originally Posted by MK27 View Post
    This is almost a non-sequiter. Who are you trying to fool, your cat?
    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.

    Here's something I read the other day, I hope you aren't offended Snafuist:
    It's extremely hard to offend me, and you certainly need more practice.

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

    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).
    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:

    Quote Originally Posted by CornedBee View Post
    "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
    Snafuist's Commentary:
    But Malbolge makes a pretty tough attempt.
    Last edited by Snafuist; 05-25-2009 at 05:29 PM.
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    Quote Originally Posted by MK27 View Post
    (but my father is Danish born and these languages are almost identical AFAIK).
    ...no

    English and Danish have more in common than German and Danish....Alot more in common actually.
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    Quote Originally Posted by Snafuist View Post
    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.
    actually, the 20 with an incorrect result
    50% were pregnant and receved a negitive result
    50% were not and received a positive result

    Quote Originally Posted by Snafuist View Post
    "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?
    no
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