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7 July, 19:09

About 8.3% of the American population has diabetes. A combination of blood tests accurately diagnoses diabetes 99.3% of the time. The tests give false positive results for 1.2% of people who do not have the diabetes. Find the probability that: A. The blood tests show that a person does not have diabetes. B. The blood tests show that a person has diabetes.

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  1. 7 July, 19:15
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    a) 90.66% probability that the blood tests show that a person does not have diabetes

    b) 9.34% probability that the blood tests show that a person has diabetes

    Step-by-step explanation:

    We have these following probabilities:

    8.3% probability that a person has diabetes.

    If a person has diabetes, 99.3% probability of the blood test showing that the person has diabetes.

    100 - 8.3 = 91.7% probability that a person does not have diabetes.

    If a person does not have diabetes, 1.2% probability of the blood test showing that the person has diabetes.

    A. The blood tests show that a person does not have diabetes.

    100 - 99.3 = 0.7% of 8.3%

    100 - 1.2 = 98.8% of 91.7%

    P = 0.988*0.917 + 0.007*0.083 = 0.9066

    90.66% probability that the blood tests show that a person does not have diabetes

    B. The blood tests show that a person has diabetes.

    Either the exam show that a person has diabetes, or it shows that a person does not have diabetes. The sum of these probabilities is 100%. So

    90.66 + p = 100

    p = 100 - 90.66

    p = 9.34

    9.34% probability that the blood tests show that a person has diabetes
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