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new brain puzzle

Discussion in 'General' started by DreamTheEndless, 17 Apr 2007.

  1. DreamTheEndless

    DreamTheEndless Gravity hates Bacon

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    Here you go:
    Please state your answer as a percentage
    (If you know what the solution is and why, don't give the reason away right away, just give the answer along with a smiley and text saying you know but won't tell - I want people to think on this one. Also - I've made it as easy as I can to arrive at the right answer.)

    A man goes to see his doctor for his standard annual checkup.

    As part of the standard checkup, the doctor performs a test that has 99 percent reliability
    - that is, 99 percent of people who are sick test positive and 99 percent of the healthy people test negative.

    The doctor knows that only 1 percent of the people in the country are sick.

    Now the question is: if the patient tests positive, what are the chances the patient is sick?​
     
  2. ch424

    ch424 Design Warrior

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    I know :)


    Edit: Oops, forgot to say it's
    50%

    Edit 2: PM me if you want the answer...
     
    Last edited: 17 Apr 2007
  3. Krikkit

    Krikkit All glory to the hypnotoad! Super Moderator

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    Someone post the answer but use spoiler tags - that'll mean no accidental views. :D

    p.s. I'm a whisker short of the answer, I know vaguely, but not fully. :p
     
  4. genesisofthesith

    genesisofthesith complete spanner

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    Got it (thanks to ch424 for giving me the answer
    of 50%
    , - had to practically work it out to 'GET IT' though :p )

    sick 1% of population

    false negative (1% of those sick) = 0.01% of population ( 0.01(sick) x 0.01(falseresult) )
    positive (99% of those sick) = 0.99% of population ( 0.01(sick) x 0.99(accurateresult) )


    Well 99% of population

    False positive (1% of those well) = 0.99% of population ( 0.99(well) x 0.01(falseresult) )
    negative (99% of those well) = 98.01% of populaton ( 0.99(well) x 0.99(accurateresult)


    So 0.99% of the general population would have a positive, and 0.99% would have a false positive.

    Hence, 50% of those that test postive are actually negative.
     
    Last edited: 17 Apr 2007
  5. ch424

    ch424 Design Warrior

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    This is my working:

    P(positive|sick) = 0.99
    P(negative|sick) = 0.01
    P(positive|well) = 0.01
    P(negative|well) = 0.99
    P(sick) = 0.01
    P(well) = 0.99

    Therefore:
    (A) P(positive) = 0.99x0.01 + 0.01x0.99
    and
    (B) P(sick AND positive) = P(positive|sick)xP(sick)=0.99x0.01
    and
    (C) P(sick AND positive) = P(sick|positive)xP(positive)
    sub values from (A) and (B) into (C)
    0.99x0.01 = P(sick|positive)x0.99x0.1x2

    Therefore
    P(sick|positive) = (0.99x0.01)/(0.99x0.01x2) = 1/2 = 50%
     
    Last edited: 17 Apr 2007
  6. kylelnsn

    kylelnsn What's a Dremel?

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  7. cderalow

    cderalow bondage master!

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    0.99%

    bugger had that messed

    80.1%
     
  8. DreamTheEndless

    DreamTheEndless Gravity hates Bacon

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    Well - either ch424 very recently took a class on the subject, or he took the answer straight off the web as he quoted the equations for Bayes' theorem exactly verbatim -
    but yeah, the answer is exactly 50%

    genesisofthesith did a very thorough and clear job of explaining it in his post. After a day or so - why don't you remove those spoiler tags, but leave them up for a bit....
     
  9. Krikkit

    Krikkit All glory to the hypnotoad! Super Moderator

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    Yep, exactly Dream. I took a class on statistical mechanics last semester, but that seems such a long time ago! :p
     
  10. ch424

    ch424 Design Warrior

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    We covered Bayes' theorem two years ago in maths at school. There's a question like that in every single S1 paper, so I'm used to doing them. I wouldn't cheat, I'm not a moron.

    However, kudos to genesisofthesith for the elegance of his answer!
     
  11. Jamie

    Jamie ex-Bit-Tech code junkie

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    Your workings are a bit of a mess there. :nono:
     
  12. ch424

    ch424 Design Warrior

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    Any suggestions for how could I do it better in future?
     
  13. DreamTheEndless

    DreamTheEndless Gravity hates Bacon

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    Yeah - I figured you had had a recent class on the subject.....

    good job everyone
     

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