Suppose there is a medical diagnostic test for a disease The

Suppose there is a medical diagnostic test for a disease. The sensitivity of the test is 0.95. This means that if a person has the disease, the probability that the test gives a positive response is 0.95. The specificity of the test is 0.90. This means that if a person does not have the disease, the probability that the test gives a negative response is 0.90 or that the false positive rate of the test is 0.10. In the population, 1% of the people have the disease. Let D be the event “the person has the disease” and let T be the event “the test gives a positive result”

(a) What is the probability that a person has the disease, given the results of the test is positive?

(b) Does this show that screening is effective in detecting this disease?

Solution

the probability of person has a diease is 0.95./1= 0.95.

this data sufficient for detecting the diease