As Bayes' Theorem illustrates, when you're testing for a rare event (e.g. a rare disease), it's unlikely that a positive result willtranslate into a high likelihood that the event happened. This is true even for tests which seem very accurate. This counter-intuitive result only works for rare events; why?Because it causes specificity to fall.Because it results in a lot of false positives.Because it causes sensitivity to fall.Because it results in a lot of false negatives.

A false positive is typically referred to as a Type I error in statistics. When someone wrongly reject the null hypothesis, then it is certainly a type I error. By assuming that the hypothesis—i.e., the alternate hypothesis—is true when it isn't, this results in a "false positive" for the study. Specificity and sensitivity are inversely proportional to each other.Because it results in a lot of false positives. In this instance, event X denotes the presence of the illness, while event Y denotes a positive test result. The likelihood of testing "false positive"—positive even when you don't have the disease—is therefore P(Y| not X). Now, the likelihood of testing "false negative" - negative even when you have the disease - is therefore P( not Y| X). Type I Error are more dreadful and specially in medical treatment when the disease is more rare the odds of really having the condition decrease as the disease becomes more rare, the test becomes less reliable, and so on. For example, if one tested positive for a rare disease (1 in 10000 people) then the probability of really having the disease may be less than 10-4 or 0.01%. The test must be population centric and does not blindly depends upon test accuracy. Thus, Option (2) is the correct answer. Explanation for wrong options: (1) This might not be the case with specificity to decrease as it is very unlikely that a disease can be detected based on test accuracy. Specificity=True negativeFalse positive+True negative (3) This might not be the case with sensitivity to fall as it is very unlikely that a wrong individual can be identified with the disease or vice-versa. Sensitivity=True positiveTrue positive+False negative (4) Since there more chances of the number of false positive to be outnumbered then the false negative results so this is also not the case.