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  • deltachamp1
    Here is the problem A medical device applied to a person known to have a disease has a 95% probability of correctly indicating that the person has the disease.
    Message 1 of 4 , Mar 2, 2005
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      Here is the problem

      A medical device applied to a person known to have a disease has a
      95% probability of correctly indicating that the person has the
      disease.

      When applied to a person known to NOT have the disease, the device
      has a 97% probability of correctly indicating that the person does
      not have the disease.

      I use the device and the result indicates I have the disease. 1 in
      2000 actually have this disease.

      What is the probability that I actually have the disease?

      -comments, i was thinking that the probability is always 1 in 2000,
      since the test is no 100% accurate, but I am probably wrong, any
      suggestions would be great.
    • rraj@tata.com
      Think of it this way - the device indicates you have the disease. This can happen only in two different ways: (a) You have the disease, and the device is
      Message 2 of 4 , Mar 3, 2005
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        Think of it this way - the device indicates you have the disease. This
        can happen only in two different ways:

        (a) You have the disease, and the device is correct
        (b) You do not have the disease, and the device is wrong

        (a) can happen with probability 1/2000 * 95 % = 0.0475 %
        (b) can happen with probability 1999/2000 * 3% = 2.9985%

        So the overall chance that a random person tests positive for the disease
        is
        0.0475% + 2.9985% = 3.046%

        Given that you tested positive, the probability of (a) being the case, is
        then
        0.0475 % / 3.046% = 1.559% - Quite a low chance of having the disease!

        Check http://www.acad.sunytccc.edu/instruct/sbrown/stat/falsepos.htm for a
        simple illustration.

        with regards,
        Rino.




        deltachamp1 <only4amillion@...>
        03/03/05 03:31 AM
        Please respond to
        probability@yahoogroups.com


        To
        probability@yahoogroups.com
        cc

        Subject
        [probability] Where do I start?








        Here is the problem

        A medical device applied to a person known to have a disease has a
        95% probability of correctly indicating that the person has the
        disease.

        When applied to a person known to NOT have the disease, the device
        has a 97% probability of correctly indicating that the person does
        not have the disease.

        I use the device and the result indicates I have the disease. 1 in
        2000 actually have this disease.

        What is the probability that I actually have the disease?

        -comments, i was thinking that the probability is always 1 in 2000,
        since the test is no 100% accurate, but I am probably wrong, any
        suggestions would be great.







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      • adia
        deltachamp1 wrote: Here is the problem A medical device applied to a person known to have a disease has a 95% probability of correctly
        Message 3 of 4 , Mar 3, 2005
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          deltachamp1 <only4amillion@...> wrote:


          Here is the problem

          A medical device applied to a person known to have a disease has a
          95% probability of correctly indicating that the person has the
          disease.

          When applied to a person known to NOT have the disease, the device
          has a 97% probability of correctly indicating that the person does
          not have the disease.

          I use the device and the result indicates I have the disease. 1 in
          2000 actually have this disease.

          What is the probability that I actually have the disease?

          -comments, i was thinking that the probability is always 1 in 2000,
          since the test is no 100% accurate, but I am probably wrong, any
          suggestions would be great.



          try to use Bayes theorem...or unconditional probability..i`m busy for my exam..i`ll atry to answer it later...u can ask at www.mathnerds.com








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        • Pedro Tytgat
          Hi, you can solve the problem by using Bayes theorem. But you don t need to know the theorem to solve the problem. It helps to think in terms of absolute
          Message 4 of 4 , Mar 5, 2005
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            Hi,

            you can solve the problem by using Bayes' theorem. But you don't need to
            know the theorem to solve the problem.

            It helps to think in terms of absolute numbers instead of probability, this
            is easier for our brains.

            Image 1000000 people. 1 in 2000 have the disease, so 500 have it and 999500
            don't have it.
            The medical test will discover 95% of the diseased people: 475 will be
            diagnosed as ill.

            Alas, the test will also incorrectly state that 3% of the healthy persons
            have the disease: 29985 people will receive this bad news.

            So in total, 30460 persons are diagnosed to be ill. Only 475 of them really
            are. The probability of really being ill when diagnosed as ill is therefore
            475/30460 = 0.01559. This is rather good news, isn't it? When the test tells
            you you're ill, you probably aren't! That explains why one usually has to
            undergo 'further tests' before the doctor will make any statement.

            When you divide all absolute numbers by 1000000, you have applied Bayes'
            law.


            Pedro


            -----Original Message-----
            From: adia [mailto:adia_one84@...]
            Sent: Friday, March 04, 2005 6:13 AM
            To: probability@yahoogroups.com
            Subject: Re: [probability] Where do I start?





            deltachamp1 <only4amillion@...> wrote:


            Here is the problem

            A medical device applied to a person known to have a disease has a
            95% probability of correctly indicating that the person has the
            disease.

            When applied to a person known to NOT have the disease, the device
            has a 97% probability of correctly indicating that the person does
            not have the disease.

            I use the device and the result indicates I have the disease. 1 in
            2000 actually have this disease.

            What is the probability that I actually have the disease?

            -comments, i was thinking that the probability is always 1 in 2000,
            since the test is no 100% accurate, but I am probably wrong, any
            suggestions would be great.



            try to use Bayes theorem...or unconditional probability..i`m busy for my
            exam..i`ll atry to answer it later...u can ask at www.mathnerds.com








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