let' nail that example home little bit more againa drug test can be common example of applying bayestheorem to prove point even highly accurate drug test can produce more false positives than true positives so in our example herewe're going to come up with drug test that can accurately identify users of drug of the time and accurately has negative result for of non-usersbut only of the overall population actually uses the drug in question so we have very small probability of actually being user of drug what seems like very high accuracy of isn' actually high enoughrightwe can work out the math as followsevent is user of the drug event tested positively for the drug so let event mean that you're user of some drugand event the event that you tested positively for the drug using this drug test we need to work out the probability of testing positively overall we can work that out by taking the sum of probability of testing positive if you are user and the probability of testing positive if you're not user sop(bworks out to ( * + * in this example so we have probability of bthe probability of testing positively for the drug overall without knowing anything else about you let' do the math and calculate the probability of being user of the drug given that you tested positively so the probability of positive test result given that you're actually drug user works out as the probability of being user of the drug overall ( ( ))which is (you know that of the population is drug usermultiplied by ( |athat is the probability of testing positively given that you're user divided by the probability of testing positively overall which is againthis test has what sounds like very high accuracy of we have of the population which uses drug multiplied by the accuracy of divided by the probability of testing positively overallwhich is so the probability of being an actual user of this drug given that you tested positive for it is only so even though this drug test is accurate of the timeit' still providing false result in most of the cases where you're testing positive