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.

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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