About 8.3% of the American population has diabetes. A combination of blood tests

Question

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:

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

Answer choices: a. 0.8802 b. 0.9066 c. 0.3415 d. 0.0934 e. 0.6685  

E) A person does not have diabetes, given that the test results were positive.

Answer choices: a. 0.1178 b. 0.4571 c. 0.1623 d. 0.3201 e. 0.0427

Explanation / Answer

B) P(blood test showing that the person hs diabetes)

= 0.083x0.993 + (1-0.083)x0.012

= 0.0934 (option d)

E) P(no diabetes | tested positive) =

P(not hving diabetes n tested poitive)/P(tested poitive)

= (1-0.083)x0.012/0.0934

= 0.1178 (option a)

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