Puzzle time: False positives
This week’s trip is over. Time to leave Florida and start skidding on icy Atlanta roads. Also time for a puzzle.
Many of you are aware that my current job involves catching fraud in online transactions. We of course focus on building systems that can catch maximum amount of fraudulent transactions. However, what you may not know is that an equal challenge in building these systems is making sure that we do not flag the good transactions as fraudulent (and irritate the good customers). This is always a tough balance. This is also called the “false positive” problem. (The test showed “positive” but that is a false result).
Here is a false positive puzzle. A village has only one lab that can perform a particular test for a particular disease. The test, however, is only 98% accurate. So, a patient who does not have the disease will get “you do not have the disease” report 98% time. 2% of the time, it will say (erroneously) say “you have the disease”. Similarly, a patient who indeed is suffering from the disease, will get a “you have a problem” report 98% of the time. The rest 2% time he or she will get a clean chit erroneously.
You also know that 0.5% of the village population has been indeed afflicted by the disease.
Your friend from the village just received a report that he has the disease.
How concerned should he be? What is the real probability that he has the disease?