Answer to Question #277413 in Statistics and Probability for JAY

Question

In a certain community, 8% of all adults have diabetes. If a health service in the community correctly diagnoses 95% of all adults with diabetes as having the disease and incorrectly diagnoses 2% of all adults without diabetes as having the disease.

Find the probability that an adult diagnosed by the health service as NOT having diabetes actually does not have the disease.                                                                                                            

Select one:

a. 0.9956

b. 0.0044

c. 0.8051

d. 0.1949

Answer 1

P(not have diabetes given tested negative)

=P(not have diabetes) $\times$ P(tested negative |not have diabetes)/P(tested negative)

$=\frac{(1-0.08) \times (1-0.02)}{((1-0.08) \times (1-0.02)+0.08 \times (1-0.95))} \\ =0.9956$