A pharmaceutical company is testing a new chemical compound

A pharmaceutical company is testing a new chemical compound that can be used to detect the presence of a disease. In the clinical trial, the company finds that 3% of the patients test positive and the rest test negative. Among the patients who get a positive test result, 90% have the disease. Among the patients who get a negative test result, only 2% have the disease. Randomly select a patient, what is the probability that he or she has the disease?

Solution

p(d|+)=0.95 p(d|+\')=0.02 p(+)=0.03

P(+\')=1-P(+)= 0.03

P(D)=P(D|+)P(+)+P(D|+\')P(+\')= (0.95)(0.03)+(0.02)(0.97)= 0.0479