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Math Help - Disease Probability

  1. #1
    Senior Member DivideBy0's Avatar
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    Disease Probability

    6
    One percent of the population suffers from a certain disease. There is a blood test for this disease, and it is 99% accurate, in other words, the probability that it gives the correct answer is 0.99, regardless of whether the person is sick or healthy. A person takes the blood test, and the result says that she has the disease. What is the probability that she actually has the disease?

    (A) 0.99%
    (B) 25%
    (C) 50%
    (D) 75%
    (E) 98%

    I thought it would just be 0.1*0.99 = 0.0099 but it appears that this is not the case.
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  2. #2
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    From the given you can see that:
    P(D) = 0.01 probability of having the disease.
    P(D^c) = 0.99 probability of not having the disease.
    P( + |D) = 0.99 probability of a positive test given the disease.
    P( + |D^c) = 0.01 probability of a positive test given no disease.

    The probability of a positive test is:
    P( + ) = P( + D) + P( + D^c ) = P( + |D)P(D) + P( + |D^c )P(D^c )

    What the question asks you to find is:
    P(D| + ) = \frac{{P(D + )}}{{P( + )}} = \frac{{P( + |D)P(D)}}{{P( + )}}.

    Can you finish?
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