Assume one in a thousand people has a particular disease. Then our prior belief is RH) = 0.001, so mnot H) 0.999 Also, assume a test to detect the disease has 100% sensitivity (i.e., no false negatives) and 95% specificity (meaning 5% false positives). Then if E repre- sents the Boolean variable "Test positive for the disease," we have P(ElnotH) Now suppose a randomly selected person tests positive, What is the prob- ability that the person actually has the disease? By Bayes theorem this is 1 x 0.001 - 0.01963 So there is a less than ( ho!) [e that d person tes;tingpositive has the disease* ror every thousand people tested, there will be on. average false positives and only I true positive. theoret)l gives us a way to the irnfiaqt of the false