bayestheorem now that you understand conditional probabilityyou can understand how to apply bayestheoremwhich is based on conditional probability it' very important conceptespecially if you're going into the medical fieldbut it is broadly applicable tooand you'll see why in minute you'll hear about this lotbut not many people really understand what it means or its significance it can tell you very quantitatively sometimes when people are misleading you with statisticsso let' see how that works firstlet' talk about bayestheorem at high level bayestheorem is simply thisthe probability of given is equal to the probability of times the probability of given over the probability of so you can substitute and with whatever you want the key insight is that the probability of something that depends on depends very much on the base probability of and people ignore this all the time one common example is drug testing we might saywhat' the probability of being an actual user of drug given that you tested positive for it the reason bayestheorem is important is that it calls out that this very much depends on both the probability of and the probability of the probability of being drug user given that you tested positive depends very much on the base overall probability of being drug user and the overall probability of testing positive the probability of drug test being accurate depends lot on the overall probability of being drug user in the populationnot just the accuracy of the test it also means that the probability of given is not the same thing as the probability of given that isthe probability of being drug user given that you tested positive can be very different from the probability of testing positive given that you're drug user you can see where this is going that is very real problem where diagnostic tests in medicine or drug tests yield lot of false positives you can still say that the probability of test detecting user can be very highbut it doesn' necessarily mean that the probability of being user given that you tested positive is high those are two different thingsand bayestheorem allows you to quantify that difference