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Math Help - Disease infection - simple probability

  1. #1
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    Disease infection - simple probability

    A disease is known to exist in 3.5% of a population. A test is 90% effective in detecting the disease, but has a 5% error-rate for "false" positive detection (an uninfected person tests positive). If the test is given to the entire population, what percent of the population would test:

    A. Positive for the disease


    B. Correctly
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  2. #2
    Senior Member apcalculus's Avatar
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    Quote Originally Posted by MathGeezer View Post
    A disease is known to exist in 3.5% of a population. A test is 90% effective in detecting the disease, but has a 5% error-rate for "false" positive detection (an uninfected person tests positive). If the test is given to the entire population, what percent of the population would test:

    A. Positive for the disease


    B. Correctly
    In the chart below D means 'disease' and ND means 'no disease'.

    ---> Positive 5% = 0.05*0.965 Branch 1
    ---> ND (96.5%)
    ---> Negative 95% = 0.95*.965 Branch 2

    Population
    ---> Positive 90% = 0.90*0.035 Branch 3
    ---> D 3.5%
    --->Negative 10% = 0.10 * 0.035 Branch 4

    A. Add branches 1 and 3, convert the number to percentage.
    B. Add branches 2 and 3, convert the number to percentage.
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