Question

a blood test is 80% effective in detecting a certain diseas when it is, in fact, present. however, the test also yields a "false positive" result for 10% of healthy persons. if 5% of the population actually has this disease, what is the probability a person has said disease when positive test result appears.

Answer 1

let A pearson has the disease peason does not have the disease B test result is positive ACA) that probability person has disease → 5% = 5 100 0.05 P(CIA) probability that test aesult is positive, if the person has the disecese 80% 80 100 = 0.8 PCB) = probability probability that person does not have the disease 95% 95 100 0.95 i 1-PCA) = 1-0.05-0.95) PCCIB) = probability that test result is positive, if the person does not have the disease 10. LO (00 0.1 probability that a pearson has the disease given that the his test result is positive PCA). PCCIN) P (ATC) PCB) PCCIB) + PCA). PCCIA) (0.05 X0.8) = (095 x 0.1) + (0.05)*0.8

= 0.04 0.095 + 0.04 0.04 M 0.135 Required probability ps 0.296