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

in mathematics, a function is a relationship between two variables such that the value of one of the variables, called the dependent variable, is determined by the value of the other variable, called the independent variable. there is a specific term we use to describe the set of independent variables of a function.